Continuity mistake: Ross is over at Chandler and Joey's looking through the peep hole for hours waiting for Rachel to return. When she does and Ross sees her go inside with Mark, Ross tries to open the door to go see her, and Chandler jumps on his back to stop him. As Chandler says "I...am not going to let you do this", Ross grabs the door handle. Then the angle changes, and as Chandler says "You...are surprisingly strong," Ross is further from the handle and grabs it again.
Continuity mistake: In the One in Barbados (part 2), just after Monica bashes her hand against the table, the shot of Chandler asking if she's OK shows Monica raising a finger right at the edge of the screen. We then cut to Monica, who's cradling both her hands together.
Continuity mistake: In the scene where Chandler sits on Joey in an attempt to regain possession of his seat, the shirt sleeve on his left arm becomes unrolled and slides down. When he stands up, the camera cuts to face Ross while he is giving out directions, leaving Chandler's back to the audience. Chandler's sleeve is now rolled back up. The sleeve remains rolled for the rest of the sequence.
Revealing mistake: Whenever Monica's apartment is shot from the point of view of the balcony looking in, fake walls have to be put up across the room to cover the open space (since there is no wall there usually). When the friends are looking out the window at Ugly Naked Guy and his girlfriend in this episode, you can see that the rear wall does not extend nearly far enough - there is a large black space behind Monica.
Continuity mistake: When they are talking about sperm donation, Joey is eating a cracker with jam on it. Between shots it instantly rotates in his hand. You can tell because the jam goes from being on the top to the bottom side, and because of the way he is holding it you can see there is only jam on one side.
Continuity mistake: When Chandler's boss is slapping all the guys on the butt, on the side of the table closest to the camera there is a tablet with a pen on it. When the guy comes back in to get his briefcase, the pen is no longer there.
Continuity mistake: Chandler walks into his apartment to find Rachel eating cheesecake without him. As the door is shutting, the pen on the Magnadoodle is hanging loose; it can be heard hitting the door when Chandler is closing it. The next shot shows Rachel stop eating, and when we next see Chandler, the door is closed and the pen is in its holder.
Continuity mistake: It's obviously December, with the set decorations and Rachel's reference to sitting on multiple Santas' laps because she is randy from her pregnancy hormones. The characters establish that it's Rachel's fourth month of pregnancy...but she became pregnant about six weeks before Monica and Chandler's May 15 wedding. Her fourth month would have been in July, not December.
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.
Visible crew/equipment: During the scene when Phoebe breaks into the other Phoebe's house and gets caught, the older Phoebe was telling the younger one that the man in the photo is not Frank Buffay, but is Chuck Mangioni. Right after that, as Phoebe 2 walks towards the camera, you can see that the door behind her moves open, and there is a visible shadow of someone who walks by that doorway.
Revealing mistake: In the scene when they confront the stripper at Chandler's office. Ross stars shouting about his grandmothers ring, and as Chandler says "way to be cool, man", you can see Joey ducking behind Ross, covering his mouth with laughter. A brief cut away, then back and he's standing with the others again looking serious.
Audio problem: When Joey is proposing to Rachel and he tells Phoebe to give him the ring back, she says "No!" and pulls her hand away. When she pulls it away, she hits her chest and there's a thump sound that's clearly the sound of her clip on microphone being hit (it's way too audible to be just a thump on her chest).
Continuity mistake: When Monica says, "I just recently got out of a serious relationship," she is holding her glass in her left hand. The camera cuts to Pete and the glass is now in her right hand. It then switches back to her left hand in the next wide shot.
Visible crew/equipment: In the scene where Phoebe knocks over the vase, after she says, "Well, that's just the way things go" and turns around to face the babies again, you can see a crew member coming out of Rachel's room. When Phoebe starts looking for the missing baby, the shadow of the crew member is visible on the right of the screen as the baby is placed in the drawer.