Corrected entry: Picard leaves the holodeck with lipstick on his face despite the established 'fact' that holodeck matter cannot leave the holodeck (eg: ST:TNG, 'Ship in a Bottle'). (00:08:30)
Corrected entry: At the end of the episode after delivering his complex greeting to the Jarada, Picard and Riker head for the Turbo lift. Just as they are about to enter, Picard opens his mouth really wide as if making a funny face to someone inside the turbolift or maybe quietly celebrating a 'successful take' given the bizarre nature of the greeting! Although it was filmed from the side it is quite easy to spot.
Correction: Picard doesn't do anything close to that in this episode. He does however do something exactly as described in the later episode "Too Short a Season", an entry for which already exists.
Correction: This must be from an outtake or alternate scene, and since it's not included in the actual show isn't "eligible" for a mistake entry (not that there's anything wrong with Picard smiling). In the episode as it was aired, at the end of the episode, after the greeting, Picard and Riker do not go to the turbolift, they sit down. However, we do see Picard smirk when he turns to the side, but also everyone on the bridge claps for him and when he turns, he's still smiling.
Corrected entry: When Picard leaves the holodeck after the holodeck character kisses him, the lipstick remains on his face. As we're told later in the episode, matter created on the holodeck cannot exist outside the holodeck. So once Picard left, the lipstick should have vanished since it came from a holodeck character. The "correction" that says simple matter can leave the holodeck is incorrect, since in another episode, they throw a book (which is simple matter) out of the holodeck and it dissolves.
Correction: The book was, as you pointed out, thrown. It was not being carried by a person. The technical manual states that many of the objects on the holodeck are in fact generated using the standard replication process. But when Picard threw the book, the holodeck simply recycled the energy from that book, the same way the food replicators recycle any food left over. When Picard walks off with lipstick on his face, or when Data walks off with a piece of paper that Moriarty gave him on "Elementary, Dear Data", the system allowed those things to be carried out without recycling them. You can take issue with what makes the holodeck decide when to recycle material or not, but the fact is simple: some simple objects can be taken off of the holodeck.
Correction: Simple matter and objects can leave the holodeck. They are created using the same technology as the replicators. There are numerous cases where matter (paper, water, food) has left the holodeck, and this is accepted as part of the technology. Complex matter (i.e. people, animals, etc.) cannot leave the holodeck. The computer might have made the lipstick transferrable for a sense of realism - no reason not to.