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.
Revealing mistake: When Monica leaves the apartment and Chandler stays listening to the answering machine, check the wall beside the door. It changes the angle, as if somebody moved it (probably to hide the hall).
Continuity mistake: Chandler and Monica are having dinner with her parents. He asks Jack how he and Judy got engaged. He starts, "Well I'd gotten Judy pregnant..." In an earlier episode they talk about how Jack told Monica's friends a "scary story" about how Judy got pregnant because her method of birth control, her diaphragm, had malfunctioned (damaged by a dog). In the rest of the show, however, we are continually hearing that the firstborn, Ross, was "a medical marvel" and that they thought Judy was barren. This apparently is the main reason why they love Ross more than Monica.
Factual error: Before Ross goes out to play the second half of the rugby game, Emily gives him some tips on how to hurt the other guys. She singles out one of the guys, saying he doesn't wear a cup. These guys are all English players who love rugby. Rugby players would NEVER wear a cup for rugby is more of a grinding sport than hit and miss. These guys would be crazy to wear a cup.