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.
Factual error: In season 4 generally, Phoebe has the shortest pregnancy ever. She gets pregnant as the boys win the girls' apartment. In the next episode Ross meets Emily, after 6 weeks he gets engaged to Emily and they then choose to get married 4 weeks later. Phoebe would only be 10-12 weeks pregnant by the time they fly to London, not in her third trimester.
Factual error: When Pete takes Monica to Rome for the date this would have been impossible as Rome is 6 hours ahead of New York and at least 4/5 hours travel time, assuming they went by Concorde (double that otherwise). They would have had to have left New York early in the morning to make dinner for 8/9 pm in Rome.
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.
Continuity mistake: In the beginning of the episode when Joey tells Chandler that he hasn't forgiven him for kissing one of his sisters, Monica and Chandler's TV, entertainment set and ferns are missing from the set and there are cables protruding from the wall. The area is completely bare except for the French poster. Everything's back to normal slightly later in the episode.
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.
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.