Character mistake: In one of the scenes where Phoebe is teaching Joey guitar, she asks him to demonstrate the "Iceberg" chord. To refresh his memory, Joey refers to the chord as "G Sharp." In reality, the only way to play a G Sharp chord is with a barre chord, and as such the fingering is not exclusive to it.
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: Right after Rachel says, "Do you know that feeling when you're trying to blow a Saint Bernard out your ass?" the camera cuts to a view of Monica and Chandler. Behind Monica and Chandler, part of the set is visible, along with a man on crutches.
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.
Revealing mistake: In the scene where Ross brings the picnic basket to Rachel's office, he lights a candle and puts it near a plant (which then sets it on fire). However, the candle is barely (if at all) close enough to set it alight, and when it does, a huge flame just erupts from the middle of the plant, not the edge where the candle was.