Continuity mistake: When Phoebe tells Ross that she wants to hear his "sound", she has her guitar in her lap. The shot changes, she says "Play that funky music white boy," and her guitar is missing. In the next shot, Ross runs out and her guitar is back on her lap again.
Continuity mistake: When Rachel is telling Monica and Phoebe about her night out with Joshua the previous evening, Monica is holding a glass of orange juice. To begin with the glass is half full, but then changes to being almost full to the top, and then back to half full.
Revealing mistake: In the scene when they confront the stripper at Chandler's office. Ross stars shouting about his grandmothers ring, and as Chandler says "way to be cool, man", you can see Joey ducking behind Ross, covering his mouth with laughter. A brief cut away, then back and he's standing with the others again looking serious.
Continuity mistake: In the episode with Chandler in a box, when Rachel is showing Ross all the things she had kept from their relationship in a shoe box, her hair is tucked behind her ear in most shots, but when she says "I keep the gifts that matter", it's all loose, then goes back to how it was in the following shot. Also in the shot before that line she's pointing the fossil at Ross, but when it cuts to a front view she's pointing it upwards.
Continuity mistake: When Chandler, Joey and Monica tell their story of the jellyfish bite Chandler says sometimes at night he still hears Joey's voice screaming "Do it ! Do it!". Joey says he yells it through the wall at night to freak Chandler out, but no nights have passed. They tell the story the same day the jellyfish bite occurred. Notice Rachel, Ross and Phoebe are wearing the same clothes they had before they left the beach house.
Continuity mistake: Phoebe and her mother are in her mother's house at the beach. Phoebe has just found out that Phoebe senior is her real mother. Have a look at Phoebe's mother in this episode and the last episode of series 3 (The One at the Beach). Her hair is a lot shorter in series 4 even though no time has passed in the storyline.