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.
Continuity mistake: Rachel tells her neighbor Danny that she doesn't know anything about sailing, but later in the series, Rachel teaches Joey how to sail after he wins a boat at a silent auction. She says she learned sailing from her father while growing up.
Continuity mistake: In the scene where Chandler turns on music when he and Phoebe are going to "have all the sex" you see Phoebe's arm begin to move in the right corner of the screen. When it cuts to her she has not yet begun dancing, and when he goes to turn the music on again it is a duplicate clip from the initial shot.
Other mistake: When Emily first walks in wearing her wedding dress, there is a distinctive difference between that dress and the one Monica picked up from the store a few episodes earlier and tried on (yes, more than that she is also wearing a jacket). There is a band of material at the top of the dress when Emily is wearing it that was not there when Monica wore it.
Continuity mistake: In the scene when Phoebe says goodbye to David, you can see Phoebe's long hair on her back. The scene goes back and forth between Phoebe and David or Phoebe and Joey (after David leaves). Each time the amount of hair on Phoebe's back changes. Sometimes it is a thin bit of hair, other times a large chunk (while the rest of her hair is framing her face in front).