Other mistake: Right at the very end, when Joey is in the fat-suit and picks up a piece of food and says "How you doin'?" he doesn't put it in his mouth, he just lifts it to his lips, stops, and tries to stay still. If this had been a freeze on the part of the director then fair enough, but it isn't as he and particularly Monica are still moving. It just looks rather corny and amateur, as though they are waiting for the "cut" to be called.
Continuity mistake: At the beginning, when Rachel first arrives at the hospital, she is talking about the hospital not being out of rooms. She points to herself with her right hand saying 'What if I was the president?' Then when the shot changes to include Ross she is pointing to herself with her left hand, then it cuts back to just Rachel and she is using her right hand again.
Continuity mistake: The first time Phoebe and Monica are making bets on when Rachel will give birth, Phoebe has a bottle of water in her hand and is holding it near her stomach. She puts it to her mouth to drink some, but in the next shot, the bottle is near her stomach again.
Continuity mistake: In the one in Barbados, part 2, when Ross and Charlie are hiding behind the plant from the other scientists, the drinks they are holding refill themselves and Charlie's ornament in her drink keeps switching sides of the glass.
Factual error: When Pete takes Monica to Rome for the date this would have been impossible as Rome is 6 hours ahead of New York and at least 4/5 hours travel time, assuming they went by Concorde (double that otherwise). They would have had to have left New York early in the morning to make dinner for 8/9 pm in Rome.
Other mistake: When Chandler, Monica and Erika arrive back at the apartment after sightseeing, Chandler enters the apartment from the left (past where their apartment door is) rather than from the right, as if he came up the stairs. He obviously is entering from the stage and didn't take the time or cue to appear to enter from the direction of the stairs.
Continuity mistake: Ross claims he looks into Monica and Chandler's and watches them eating dinner and watching TV. His apartment is a floor lower down than theirs and with the balcony wall, the sofa and tables distance from the window and the fact the bottom of the window is higher than the floor, there is no way Ross would be able to see that far in. We have seen in the past that he can basically only see who is at the window.