Continuity mistake: Rachel takes the cat to apartment number 8 and Mr. Heckles opens the door. However, in this episode, the girls' apartment is labeled number 5 which means that number 8 is above them. In later episodes, Mr. Heckles always says that the noisy girls upstairs are keeping him from doing things. [It makes a bit more sense later on in the series when Monica and Rachel's appartment changes to number 20, which is when Mr Heckles starts to complain about the noise (although in the flash back episode when Phoebe is still living with Monica it seems apparent that they actually know Mr Heckles, which Phoebe shows no sign of when she and Rachel are looking for the owner of the cat).]
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).
Continuity mistake: During the Monopoly game (deleted scene), right after Monica says, "we can bring my wheelbarrow, to carry your teeth," we see Ross reading the game manual at the end of the shot. At the beginning of the very next shot, he is suddenly rolling the dice with no manual in his hands.