Continuity mistake: In the scene where Phoebe asks Mike to prove that he plays piano, his arm goes from resting on the couch to on his lap from one shot to the next. After Phoebe tells him "You are really good," his left arm is resting on the couch. But in the next shot when Phoebe continues talking, his arm is resting on his lap.
Continuity mistake: When Jack and Judy leave Joey's apartment, there is a birthday banner on the counter that has fallen off. When Monica, Chandler, Joey and Phoebe are racing the toys to see who gets to go, the banner is back on. In this time no-one has fixed the banner as there is not enough time for them to do so off camera and the people on camera don't fix it. It's most clear that it's back on when Monica is saying, "Technically, our dog never crossed the finish line".
Other mistake: There are two mistakes in the scene where Phoebe spots Joey's picture in the laundromat. For one thing, when Phoebe says "Oh, here it is", she is looking in the opposite direction of the picture. Also, when she says this, her mouth doesn't move at all.
Continuity mistake: In the scene where Ross takes a liquorice from the skull, in the first close up shot he is holding it in his hand, but then immediately after this when they zoom out, he is chewing a piece. This is impossible because he would have had no time to bite it.
Continuity mistake: During the scene when Chandler arrives with his test results, Phoebe is reading a book with a red section on the left hand page. In the next shot, the red on the page has vanished. Then, in the next shot, the red page is back again. Also Phoebe's left hand moves between shots.