Character mistake: Both lightning rounds at the end of the quiz are significantly longer than the 30 seconds that Ross claims they are. (Even though he is supposedly using a stopwatch to time them.) The guys' lightning round is actually 43 seconds long, and the girls' lightning round is 45 seconds long.
Continuity mistake: When Rachel and Phoebe are in Central Perk talking about the Princess Leia Fantasy, a guy in a yellow shirt and white pants is standing at the bar behind Phoebe. As they talk he walks to the door and leaves, but in the next shot he is standing behind Phoebe again, just as she says "That's the moment when she becomes a woman."
Continuity mistake: At the beginning when Rachel and Monica talk about the free coffee sample, Rachel puts it down on the counter to her right. In the next shot it's lying to her left with no time to have gotten there. After that it switches from the right to the left and back again.
Continuity mistake: When Joey brings his date home and Monica runs into the bedroom with Chandler, her foot dislodges a red pillow that is very close to a candle on the floor. As the scene goes on, the pillow alternates between being kicked out of place and being neatly arranged with the others.
Continuity mistake: In the scene where Phoebe tells the gang about her "Relaxitaxi" idea the position of Chandler's left arm changes between shots. In the frontal shots it's lying the back of the chair and in the shots from behind it's wrapped around Monica's shoulder.
Other mistake: When Ross is at Monica's party getting Mr. Green's glasses and cigarettes he bumps into Mrs. Green and ends up having to come up with an alibi for the glasses and cigarettes. He then puts the glasses on, puts a cigarette in his mouth and says 'In fact I'm gonna go out into the hallway and fire up this bad boy'. At this point he walks past Rachel but he stops still as if frozen mid-step just before the shot cuts to him walking out into the hallway.
Factual error: Joey and Chandler are supposedly crossing the George Washington Bridge but the exterior background viewed from inside the car is very obviously a repeat reel of another bridge, and their conversation goes on for far too long for the actual crossing. And the cutaway shot after Chandler is kicked out of the car shows an aerial view of the Brooklyn Bridge.
Visible crew/equipment: When Chandler runs into the apartment to say Underdog has gotten away, a crew member can be seen reflected in the sun shaped mirror behind him walking through the back of shot. It can't have been Rachel, Monica, Phoebe or Joey because Joey is sitting down and Rachel, Monica and Phoebe are nowhere near the mirror.
Other mistake: When Chandler, Monica and Erika arrive back at the apartment after sightseeing, Chandler enters the apartment from the left (past where their apartment door is) rather than from the right, as if he came up the stairs. He obviously is entering from the stage and didn't take the time or cue to appear to enter from the direction of the stairs.