Revealing mistake: When Phoebe is looking at the front page of the "Chelsea Reporter," Monica says her restaurant review is on the back page. However, Phoebe doesn't turn to the back page, but merely flips the paper over, looking at the bottom of the front page (and finding the review there).
Continuity mistake: There is a scene in Central Perk where Rachel confronts Chandler about all the kissing he's been doing. She raises her hands up in front of her and tells Chandler to hold on to stop him from getting up from the couch. As he goes to sit back down on the couch she lowers her hands to her lap. The shot cuts to an angle behind Rachel's chair and she is lowering her hands again.
Revealing mistake: When Monica and Phoebe are in Central Perk, Phoebe is looking through the list of ideas that Monica has come up with for the use of Phoebe's van. If you look closely (most obvious just after Phoebe says "let's plan the wedding reception") you can see that every single page of the notebook Phoebe is holding has the same thing written on it, instead of lots of different ideas that Monica is meant to have had.
Continuity mistake: Phoebe and Ross are in the soon to be closed bar sitting on the pool table. He clears it of everything, but a few seconds later he stops making out because the "damn balls are in the way" and somehow magics up a handful of snooker balls. If you look closely when he's clearing the table, there are two dark balls at the side which he studiously ignores, and which Lisa Kudrow then surreptitiously grabs and takes onto the table with her so David Schwimmer can grab them later.
Other mistake: In series 8, 'The One with the Videotape,' when they are watching Ross and Rachel on the TV and when Rachel (on the video) is discussing the invitations and how Monica didn't shut up about sending them, Chandler points at the TV and makes a kind-of confused face. A few minutes later, just before he says 'Did you do it on our invitations?' the same shot of him pointing and pulling a face comes up.
Continuity mistake: Right before Ross and Rachel storm in, the girls show Joey how much their waxing stuff hurts. Phoebe starts putting the wax on Joey's inner arm, but then the shot changes and she is spreading in on the outer side. Also she slaps the strip on and the blue tab is hanging down off his arm, but then the shot changes again and it is on his arm with the other end of the strip hanging off the other side.
Revealing mistake: When Monica offers Joey lemonade and he takes off his clothes and is behind the lamp, the tops of his boxer shorts are visible when he says "Were you just gonna give me lemonade?" Broadcasts may crop off this bottom part, DVD doesn't. You can also see his gray boxer shorts through the plant in the previous shot.