Continuity mistake: When Ross comes back to Monica and Rachel's apartment and Rachel tells him she has lost Marcel, he takes off his overcoat and lays it over the back of the sofa and then sits by it. In the same scene, when the animal control lady arrives, Monica and Phoebe have joined them and they are standing round in the kitchen area. The sofa is still visible in the background but the coat has disappeared without anyone having been near it.
Continuity mistake: In the scene where Monica is explaining to Rachel that she has hired her friend Wendy as her waitress, Rachel is holding a water bottle in one hand and the cap in the other. Monica moves towards her and Rachel is pointing her hand in Monica's direction and then in the next shot we see Rachel from another angle and her hand is holding the cap on top of the bottle too fast to have happened in normal time.
Continuity mistake: Rachel and Phoebe are in the Central Perk, talking about leaving the group, and a jacket and a handbag are hanging on the arm of the chair behind Rachel, slightly to her left. Between shots it changes from just the jacket, then just the handbag and so on. This continues throughout the scene when Ross comes in and Phoebe leaves. As she gets up you see both again, however Rachel does not move enough to just show one and hide the other.
Continuity mistake: When Monica, the fake Monica and Rachel are in the girls' apartment talking about the two Monicas auditioning for CATS, Monica (real) has a baguette and a bowl of sandwich filler on the table. In one shot of all three of them, she opens the baguette and starts filling it, then the camera goes in for a close-up of the real Monica and she opens the same baguette and starts filling it again.
Continuity mistake: When Monica and Chandler are in Las Vegas watching the burlesque show, Chandler turns the light on the middle of the table off to "hide" from his Dad. When Monica calls out saying "Waiter. Waitress.", the light is suddenly back on and remains on for the rest of the scene.
Continuity mistake: When Ross and Rachel are arguing about Rachel telling Phoebe about his fantasy, Ross takes a popsicle out of the freezer and bites it. In the next shot, the popsicle is whole again, with no bites, and Ross takes another 'first' bite out of it.
Continuity mistake: When Ross is telling Monica and Phoebe that he found his "sound" in college, Monica spits out her orange juice and places the glass on the coffee table. The shot changes to Phoebe and you can see Monica putting the glass down again.
Other mistake: Ross makes up the questions for the quiz. There are two groups of questions, one for the girls and one for the boys. Each one has four categories; there are four questions in each category. From these 16 questions, Ross asks ten. Thus, there have to be six left after the quiz. But in one group, seven questions can be seen (there are seven cards left).