Character mistake: After the guys have beaten the girls in the quiz, Rachel refuses to move apartments and Monica says: "If we had lost, we would have made them get rid of the birds." But they did lose. That's why the guys have got their apartment. She should have said if we had won.
Character mistake: In one of the scenes where Phoebe is teaching Joey guitar, she asks him to demonstrate the "Iceberg" chord. To refresh his memory, Joey refers to the chord as "G Sharp." In reality, the only way to play a G Sharp chord is with a barre chord, and as such the fingering is not exclusive to it.
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.
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.