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).
Other mistake: Right at the very end, when Joey is in the fat-suit and picks up a piece of food and says "How you doin'?" he doesn't put it in his mouth, he just lifts it to his lips, stops, and tries to stay still. If this had been a freeze on the part of the director then fair enough, but it isn't as he and particularly Monica are still moving. It just looks rather corny and amateur, as though they are waiting for the "cut" to be called.
Continuity mistake: Ross claims he looks into Monica and Chandler's and watches them eating dinner and watching TV. His apartment is a floor lower down than theirs and with the balcony wall, the sofa and tables distance from the window and the fact the bottom of the window is higher than the floor, there is no way Ross would be able to see that far in. We have seen in the past that he can basically only see who is at the window.
Visible crew/equipment: Just after Chandler says "I'm the smallest person in the world", and Joey comes out of his room, check the top left of the screen - you can see a boom mic track Matt LeBlanc across the set, and the bottom of some stage lights in the middle.