Continuity mistake: In the scene where Monica and Ross walk in carrying a few carrier bags, Monica takes out a pack of green plates, but in the next shot she is holding 4 packs of plates - 2 green, 2 red. She did not have time to pick up another pack between shots.
Revealing mistake: When Phoebe says something like, "Look, the last candle is about to go out", she starts counting down, saying "-47,-48..." and you can see Monica looking at the candle. But there is a light source behind her (it can't be a candle because she is looking at the last candle).
Revealing mistake: When Emma starts crying and Rachel picks her up, look at how much the baby is moving when she takes it out of the cot. In the next shot it's suddenly only moving it's head, and very slowly at that. This is because it's a robot - and it's very obvious.
Continuity mistake: When Joey walks back into the apartment (with his eyes covered) to get the sandwich, he walks by the Fussball-table, and there's nothing on it. When he walks away you see a purse lying on the cooker. Then, when the shot changes to Dina and Rachel, you see the purse lying on the fussball table.