Continuity mistake: In the scene where Joey is showing kids around the museum, there's a little boy who corrects Joey about the existence of the Mastodon. The kid's arm is by his side at the beginning of the scene. When he begins saying, "Isn't the Mastodon from the Pliocene Epoch?" his left arm is suddenly up and his thumb pointing at the Mastodon.
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).
Continuity mistake: S3E1; Ross is telling Chandler about how woman tell each other everything in Central perk. Chandler puts a book about trout on the table and then talks to Ross, then the camera zooms out and the book has moved more to his left and a coffee mug is in front of it.