Continuity mistake: When Ross turns on the camera and sits down in front of it, "flirting" with it and drinking wine, what you can see on the little camera screen is very different from when they play the same clip on the TV, in which looks like he was sitting much closer to the camera then he actually was.
Visible crew/equipment: In the scene where Phoebe knocks over the vase, after she says, "Well, that's just the way things go" and turns around to face the babies again, you can see a crew member coming out of Rachel's room. When Phoebe starts looking for the missing baby, the shadow of the crew member is visible on the right of the screen as the baby is placed in the drawer.
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.
Continuity mistake: Monica chooses a wedding dress at an expensive boutique, then later goes to a discount store to buy the same-style dress at a half-off sale. The dress she buys is different from the one in the boutique, having wider and frillier straps. When she tries it on later at the apartment, it is now the same style as the one at the boutique.