Continuity mistake: As Chandler is writing on the board to remind himself about Joey's audition, the door opens as he's writing "Joey", and there are a bunch of squiggly lines under the y. As Chandler is thinking back at that moment and it moves to present tense, he looks over to the board, and the squiggly lines are different.
Continuity mistake: When they're all sitting together and having pizza, talking about parents, Rachel has no napkin. When she says: "Just think, in a couple of years we get to turn into them", a bunched up napkin appears beside her on the couch. After Chandler's remark it has disappeared again, then it appears and reappears again between shots.
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.
Other mistake: When we see the chess board at Central Perk that Ross and Chandler are using, the black pawn in front of the black knight nearest the camera is missing, and from the arrangement of the white pieces, it cannot have been captured yet.
Visible crew/equipment: In the scene where Chandler pretends that he just got home from Tulsa and meets Joey who is waiting in the hallway outside the apartment, the camera cuts between Chandler and Joey. Every time the camera shows Chandler, there is a wooden wall at the left edge of the screen with an orange tape. This is evidently part of the set, because when the camera cuts to Joey, the wooden wall with the orange tape is nowhere to be seen.
Revealing mistake: In the scene where they are in the coffee shop talking about Rachel's dream about Chandler. Rachel is carrying a coffee pot around then sits down. When she sits she puts her hand under the coffee pot, which would be extremely hot if it were real.
Continuity mistake: Ross buys the Ultimate Fighting Combo, a large pop and popcorn at the fight, but when he and Monica sit down, they are never seen again. Furthermore, when Monica talks to Pete at the ring, you can see that the Combo was not set on the floor.
Visible crew/equipment: When Joey and Chandler walk into their apartment and the table falls over when Joey puts the key on it, the edge of the set and studio lighting are visible at the top of the screen. In the widescreen version, the end of the set wall is visible at the right side of the screen.