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.]
Audio problem: The camera cuts briefly to Chandler as the friends are discussing Monica's love life. During this very brief time, you can see Phoebe's mouth moving but there is no audio of her voice, and Monica's voice is heard talking in the background instead. (00:01:10)Zyen Hoo
Continuity mistake: When Ross shows Chandler and Joey the can of "Carol's favorite beer" it's unopened as Ross makes a crack about how he "should have known," but in the next shot we see Ross lifting the can and drinking from it, even though he never actually pulled open the stay-tab between the two shots (viewed in widescreen). (00:09:55)Super Grover
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: Before Monica stomps on Paul's watch, the chair closest to the fridge does not have fabric backing, then when Ross eats the Oreo and walks toward his jacket the chair closest to the fridge is now fabric backed and his jacket hangs from a chair with no fabric, plus there are only four chairs around the table. However, when Ross picks up his jacket this chair is now fabric backed, the chair closest to the fridge doesn't have a fabric back yet again, and there are now five chairs around the table.Super Grover
Continuity mistake: While Joey and Chandler are at the apartment with Ross, a watch suddenly appears on Joey's wrist when he announces that he and Chandler are done with the bookcase, then the watch vanishes and reappears again in the following shots at the apartment.Super Grover