The Nitpicker's Guide for Next Generation Trekkers, written by Phil Farrand, is a classic work of Star Trek commentary discussing inconsistencies and bloopers from throughout the series. (In fact, I must credit Mr. Farrand for inspiring the name of this blog - he has a subheading called "Ruminations" in his discussion of certain episodes.) The problem of holographic objects leaving the holodeck is touched on throughout the book and finally summed up in his entry on the sixth season episode "Ship in a Bottle":
If holodeck matter cannot exist outside the holodeck, the following anomalies exist.  Wesley, drenched in Holodeck water, walks off the holodeck and remains wet in "Encounter at Farpoint."  Picard, kissed by a 1940s holodeck woman is "The Big Goodbye," leaves the holodeck with her lipstick intact on his cheek.  During "Angel One," a snowball flies out of the holodeck and hits Picard.  And finally, Data carries a piece of holodeck-created paper to a meeting of the senior staff in "Elementary, Dear Data."Farrand points out (in his earlier discussion of "Elementary, Dear Data") that the Star Trek: The Next Generation Technical Manual makes a "valiant effort" to reconcile what happens in these episodes with the clear statements made about how holographic objects cannot leave the holodeck. But, in his opinion, the effort wasn't good enough. While I am not going to rehash all of his reasoning here, he demonstrates that the specifics of the Technical Manual's explanation are not consistent with evidence from the episodes themselves.
However, I would argue that there is a way to reconcile the four "anomalies" Farrand describes with what we know of the holodeck. In fact, the visual and logistical evidence suggests that at least some of what the Technical Manual says was on the right track - just not applied in a way that was consistent with the show itself. I will first attempt to outline the premise of my theory and then demonstrate how it applies in the episodes in question.
"Automatic Updates Available Now"
In the 21st century technology is upgraded and improved faster than most of us can keep up with it. It makes sense that this would also be true in the 24th century. The episode "11001001" (TNG) actually shows us the holodecks receiving an upgrade, and we can assume that there have been many other upgrades - both in hardware and software.
The look of the holodeck itself has changed from the yellow on black grid of TNG to the metallic framework seen on Voyager. When I first saw the "new" holodeck on Voyager I thought, "That's not a holodeck. Holodecks don't look like that." That's probably nostalgia on my part for the days when TNG was first on the air. I also think their is something visually striking - something classic - about the clean lines of the original look. But whichever look you prefer, the technology clearly changed over time.
This means that the way a holodeck works in one episode does not have to be identical to the way a holodeck works in another episode set a year or two later. In fact, it would be unusual if it did always work the same way. While we should expect some broad level of consistency, we should not demand every detail to always be the same every time a holodeck is used. Technology changes. I will refer to this concept as the Upgrade Principle.
Not Everything on a Holodeck is Hologram
During the seven year run of Voyager the phrase "photons and forcefields" was thrown around as a description of the Doctor and holograms in general. In the episode "The Phage" the Doctor demonstrated what this means by slapping Paris and then asking Paris to slap him. As a hologram, the Doctor could have as much or as little "substance" as he wanted - he hit Tom, but Tom's hand passed right through him. (He pulled a similar trick when he was attacked with a sword in the episode "Heroes and Demons.")
Evidently photons and forcefields are used to create most of the inanimate objects on the holodeck. And it appears to be the only way to create a holgraphic character, this is to say any thing "living", whether human, alien, or animal. The gangsters in "The Big Goodbye" (TNG), the book Picard throws though the doorway in "Ship in a Bottle" (TNG), and the Doctor's arm in "Projections" (VOY) all disappear when they leave the holodeck. These are all examples of holograms, that is to say simulations made of "photons and forcefields." They depend on the holoprojectors to maintain the illusion of substance.
(Clearly the disappearing gangsters must have been photons and forcefields because as their feet and legs disappeared they remained suspended in the air. A physical object would have collapsed. That the disappearance of the gangsters was less abrupt than the other two examples mentioned here can simply be explained with the Upgrade Principle. Evidently later holoprojecters behaved somewhat differently.)
I would argue that all of the statements made by Picard and others to the effect that 'holgraphic matter' cannot leave the holodeck are referring to this concept of holograms. In other words, the expression 'holographic matter' is basically a euphemism for that which appears to have substance on the holodeck but is actually made out of photons and forcefields.
On the other hand, some objects on the holodeck clearly are not made of photos and forcefields. Instead they must be replicated matter - completely real and solid. To reach this conclusion we simply have to refer to all the statements about 'holographic matter.' If 'holographic matter' cannot leave the holodeck, then anything that we have seen leaving the holodeck by definition could not have been 'holographic matter'. And since these were not objects brought onto the holodeck by the crew (such as the costumes or sports equipment we sometimes see them wear or carry onto the holodeck), these object must have been replicated by some system within the holodeck itself.
Beyond that general reasoning, there is other evidence demonstrating that, at least in some instances, replicated objects appear on the holodeck. In the episode "Ship in a Bottle" (TNG), Data throws his communicator at the holodeck wall to demonstrate that they are, in fact, still on the holodeck. When it hits the wall it causes a disruption in the holographic image and falls to the ground. This indicates that - at least in situation where the simulation is not programmed to account for it - real, physical objects can disrupt the holodeck if they are suddenly thrown at one of the walls.
Now compare that to what we saw in "Encounter at Farpoint." Data throws a rock. It hits the holodeck wall and disrupts the simulation. This strongly suggests that the rock was not a hologram (photons and forcefields). Evidently it was an actual rock (okay, an actual, replicated rock). And if the rock was replicated, it stands to reason that other objects on the holodeck may have been replicated as well.
Also, consider the matter of food on the holodeck. In the Nitpicker's Guide, Farrand refers to the crumpets Moriarty serves to Dr. Pulaski in "Elementary, Dear Data": "When she leaves, does that matter evaporate? (I know some people who would think this wonderful. Enter a holodeck. Gorge yourself. Walk out, all gone!)" His offhanded remark actually highlights a strong argument that the holodecks can and do produce replicated matter.
On one hand, it is conceivable that holographic food could be ingested, sit in your stomach, and then later disappear. Compare B'Elanna's holographic baby in the episode "The Killing Game" (VOY). This seems like a fairly sophisticated use of the holodeck, perhaps one that was not always possible (in line with the Upgrade Principle) but, at least by the time of Voyager, it was possible to have holographic food.
On the other hand, it isn't probable that the crew would want to eat food that wasn't real. Think of all the food and drink the crew had at Sandrines or at the pub in Fair Haven. Think about Seven of Nine's lobster dinner in "Someone to Watch Over Me" (VOY). Surely most - if not all - of these must have been actual, replicated meals. (If someone consistently ate disappearing, holographic food I could see it becoming some kind of 24th century eating disorder - call it holographic bulimia. Barclay would probably end up with it.)
So while there may not be specific dialogue establishing it, the above points demonstrate that holodecks interface to some extent with the ship's replicator system. This brings us back to the Technical Manual, which says the holodeck has a "matter conversion subsystem" that creates physical props as well as a "holographic imagery system" that uses "shaped forcebeams" to create the illusion of objects with substance. Its subsequent explanation of how the two systems interact may be flawed in comparison to the show itself, but the basic premise must be true. There must be replicated matter on the holodeck. The question then becomes, when and why does the holodeck use the matter conversion subsystem?
All Together Now
If we put together the Upgrade Principle with the premise that objects (but not living matter) can be created by the replicators, a theory rather naturally suggests itself. While the holodecks have always had both capabilities, and evidently still do, it seems that early on they relied much more heavily on replicated objects. The "shaped forcebeam" technology (the photons and forcefields system) was not as refined early in the history of the holodeck. As time went on, more and more things were created as holograms, but for some items (especially food) replicated objects were still more feasible or desirable to the user. This rather neatly explains why these supposed inconsistencies cropped up early in the run of TNG - not because the writer's hadn't figured it all out, but because the technology itself was not as sophisticated at the time. Now, let's apply this theory to the specific "mistakes" Farrand identified:
1. Wesley's Water "Encounter at Farpoint" - We have already considered that at least some of the rocks in this simulation were replicated rocks. Since the water was able to leave the holodeck it also must have been replicated. We know from "Caretaker" (VOY) that starships can replicate large quantities of water very easily. On the other hand, getting forcefields to imitate water may be a considerable challenge. Getting just the right feel of its wetness, surface tension, and so on was perhaps impractical or even impossible in the early days of holodeck technology. In fact, water may still be replicated on a fairly regular basis since someone going for a swim or walking along a holographic beach may want the experience of really getting - and even staying - wet.While there is some seeming confusion about holographic matter, I believe that this theory adequately addresses the basic premise of how a holodeck functions as well as the specific problems pointed out by Mr. Farrand. And, if we are very generous, we can even choose to believe that the writers knew this all along. As Mr. Farrand put it, "The Creator is Always Right."
2. Picard's Lipstick "The Big Goodbye" - Again, the limitations of early holodeck technology may have come into play. The subtle texture of a thin layer of lipstick left on a person's cheek may have been beyond the capability the holodeck to duplicate convincingly with forcefields. Alternatively, the programmers of the Dixon Hill holo-novels may have intentionally included replicated lipstick as a kind of practical joke on the wanna-be private investigators out there.
3. The Snowball Effect "Angel One" - This is very similar to the liquid water in "Encounter at Farpoint." Image trying to simulate millions of little snowflakes, with all their facets, how they stick to each other, how the slide over each other, how they fall apart. We can conclude that this was beyond the system's capabilies so it replicated the snow. Also, serious skiers may feel that holographic snow just doesn't feel right - that it's not enough like the real thing. So they use the replicators to conjure up real snow.
4. Moriarty's Sketch "Elementary, Dear Data" - This fourth case is admittedly harder to rationalize. It happened later than the other three and involves a rather simple object - a piece of paper. It would be difficult to argue that the holodeck couldn't simulate a piece of paper. Yet this paper left the holodeck, so it could not have been a hologram. So why would it have been replicated? Consider two possibilities.
First, this may have been a feature of the Sherlock Holmes programs in general. Perhaps whoever devised the stories saw some entertainment value in actually replicating certain props, certain clues, for the participants to find and even keep as "souvenirs" of some kind. This way they could collect trophies from all the cases they solved, just as Holmes collected significant items from his cases.
A second idea revolves around the unique situation in this episode. The computer created a hologram with ability to beat Data. This granted Moriarty sentience and a measure of control over the holodeck. He could even call for the arch. Perhaps he also had access to the matter conversion subsystem and had been experimenting with conjuring real - albeit lifeless - objects, and this paper just happened to be one of them. Or he may have intentionally created this for Data as a demonstration that he was a force to reckon with. In any event Moriarty's case is so unique we should not be surprised that other unusual holodeck activity was associated with this incident.