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.]
Visible crew/equipment: When the guy delivers the wrong pizza, in the shot after Monica grabs the pizza box to hand to Phoebe and shouts that they have George's pizza, the tape marks can be seen on the floor with one of them between the delivery guy's feet.Super Grover
Visible crew/equipment: While Phoebe's talking about David she mentions the movie 'An Officer and a Gentleman, ' and when she tells them that David is kind of like the guy she went with to see that movie, in the following wideshot the boom mic can be seen moving around at the top of the screen. (00:06:10)Super Grover
Visible crew/equipment: After Monica asks Rachel if there's someone else and shouts, "Why the hell are you dumping my brother?," when it cuts to Chandler sitting at the counter, the edge of the set can be seen at the left side of the screen, and also note the front door is wide open for the camera access. Additionally, when Joey joins Chandler at the counter the juice box has black tape covering its brand name.Super Grover
Visible crew/equipment: When everyone walks in while Ross and Rachel are talking, just as Joey says that he doesn't need violence to enjoy a movie, in the small mirror behind Joey we can see the reflection of equipment moving, presumably a reflector screen.Super Grover
Visible crew/equipment: When Ross announces that Carol's pregnant, after Chandler says, "Kind of puts that whole pillow thing in perspective..." in the next shot of Ross and Monica we can see a crew member's sleeve at the left side of the screen.Super Grover