Continuity mistake: When Rachel finds out that Ross and Julie are getting a cat, watch Rachel's tray. When she says "together?" she's got a towel that is flat; cut to Ross and Julie for a fraction of a second, then when it cuts back to Rachel saying "both of you?" it's now in a pyramid.
Continuity mistake: In the second scene with Phoebe and Rachel in the night class, when the camera looks over Rachel's shoulder, she has "Jane Eyre" in her hand face up, but when the angle switches to front view, she has nearly placed the book on the desk.
Other mistake: This is the episode where a guy across from Monica's apartment is spying on them. Joey says he caught him spying into his and Chandler's apartment yesterday. This is impossible considering the layout of the building i.e. the fact that the only part of Joey and Chandler's apartment which faces toward the spying guy has the stairwell and hallway blocking it from view (not to mention the protruding part of Monica's apartment). There is another window in Joey's apartment but it faces completely the wrong direction. The bathroom has no windows. The angles just don't add up.
Continuity mistake: When Joey and Angela talk in Central Perk, the black waitress with long hair is visible the background of shots of Angela. When we see shots of Joey the same waitress is also behind him near Gunther. She is in two places at once.
Audio problem: As the nurse comes back from wrapping the new baby, we hear her say "Here she is," yet her mouth doesn't move to the words she is apparently saying. Even though her mouth is only visible during the "she is", she's not saying the words. Then she mouths some sort of "oh", but nothing is heard.