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.
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).
Character mistake: After the guys have beaten the girls in the quiz, Rachel refuses to move apartments and Monica says: "If we had lost, we would have made them get rid of the birds." But they did lose. That's why the guys have got their apartment. She should have said if we had won.