Other mistake: When Rachel arrives at Central Perk, Monica introduces her to everybody, including to Chandler, as if they don't know each other. In later episodes, we learn that Chandler met Monica and Rachel a couple of times when they were in high school (including when Monica cut his toe off). Chandler even kissed Rachel once, and since Chandler always says that he hasn't kissed many women, he should have perfectly remembered Rachel, and Monica should have remembered that the two of them knew each other.
Continuity mistake: The number of the flats near the start of the first series was 4 and 5. After a few shows they changed to 19 and 20. [The producers realised that the numbers 4 and 5 were for apartments on the lower floors and had shown Monica's apartment to be much higher up so they changed the numbers - it's still a mistake but there's the reason.]
Continuity mistake: After Marcel has escaped from the basement, he is seen eating a banana as a pair of arms reach out to grab him. These arms are supposed to belong to Mr Heckles, their weird neighbour, however the arms clearly belong to a young, large and hair free woman.
Continuity mistake: When Monica takes off her belt and throws it onto the couch, it lands on Rachel's arm. Throughout the scene, between shots of Rachel and Monica talking, the belt constantly disappears, reappears and changes position without Rachel ever touching it.