Continuity mistake: In the one where Ross finds out he's having a boy (series 1), just before Rachel lets it slip, she is sitting on the edge of a chair eating a cookie. Watch her dress, it changes back and forth from being undone from the waist up, to only having two buttons open at the top.
Continuity mistake: When Monica comes in and asks Chandler if she can borrow some milk, Chandler is reading a paper that is flat on the bar. In the next shot he is holding it folded, then he lays it on the counter, and suddenly it is in his hands again.
Visible crew/equipment: During the scene when Phoebe breaks into the other Phoebe's house and gets caught, the older Phoebe was telling the younger one that the man in the photo is not Frank Buffay, but is Chuck Mangioni. Right after that, as Phoebe 2 walks towards the camera, you can see that the door behind her moves open, and there is a visible shadow of someone who walks by that doorway.
Continuity mistake: In the beginning of the episode when Joey tells Chandler that he hasn't forgiven him for kissing one of his sisters, Monica and Chandler's TV, entertainment set and ferns are missing from the set and there are cables protruding from the wall. The area is completely bare except for the French poster. Everything's back to normal slightly later in the episode.
Continuity mistake: Joey is watching Ross from Monica's window and goes searching for the hot girl. The exterior shot crossing the street between buildings is inconsistent with the interior shots, which show them looking at each other across an alley with no visible fire escapes. The exterior shot crosses a street to a building with street-facing fire escapes on every apartment.
Factual error: Joey and Chandler are supposedly crossing the George Washington Bridge but the exterior background viewed from inside the car is very obviously a repeat reel of another bridge, and their conversation goes on for far too long for the actual crossing. And the cutaway shot after Chandler is kicked out of the car shows an aerial view of the Brooklyn Bridge.
Continuity mistake: In the scene where Ross and Carol are talking and Carol says that all he needs is to find a woman who likes men, a woman comes across the room walking in high heels. The shot is wrong because we see her up until she's half the way through the table, and the next shot shows her four steps back.