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.
Continuity mistake: When Rachel and Monica are discussing whether or not Rachel should meet Ross at the airport she's taking a bottle of red wine out of the refrigerator, but when she places it on the table in the next camera shot the bottle of wine is suddenly a bottle of white wine.