Continuity mistake: When Phoebe goes to visit her mum for the first time, before she takes the photo off the fridge the cookie jar has its lid on. After she has taken the photo off the fridge, the lid has come off the cookie jar though there is no way Phoebe senior could have taken it off.
Continuity mistake: When Chandler is telling Monica and Phoebe about the girl who picked him over Joey, look behind him and you will see Gunther nodding to a lady in a denim jacket. In the next shot, the woman walks up to the counter again, and again Gunther is nodding at her.
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.
Continuity mistake: In the last scene, Chandler is sitting on the couch in the new apartment, and the rooster is sitting on the back of the couch, with his tail facing the window. When Joey comes running out, the shot of the rooster shows his face toward the window, and then in the next shot he has returned to his tail facing the window.
Factual error: Monica takes an ovulation test to see if she is still ovulating. The ovulation test only works before you ovulate (usually 24 to 36 hrs), to detect the LH surge that comes before you ovulate. Once you ovulate that surge is gone and the test will not work.
Revealing mistake: When Rachel is doing the shuffling trick, it is clear that it is a trick deck. The cards, whilst flying from one hand to the other, change the angle of flight in mid-air, and some of them even move backwards as she moves her hands further apart from each other. This could only happen if the cards were connected to each other.
Visible crew/equipment: When Monica is waving around her shellfish hairdo in the final scene at the hotel, the camera zooms out. When it does this, look at the top of the set. Not only can you see where the set ends, but you can also see the stagelights, hanging equipment etc.