Visible crew/equipment: In the scene where Ross and Joey are explaining phase two of Chandler's break up (going to strip clubs), the camera switches from the girls to Ross and Joey. Behind them is Monica's kitchen window where you can briefly see a reflection of someone passing by (crew member). At first I thought it could have been Chandler, since he was not in the scene, but after a few moments you see that Chandler has been in the bathroom the whole time.
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.
Continuity mistake: In the opening scene Rachel is holding a white felt pen in her hands and gesturing with it while she talks about the soap opera digest magazine. Between shots the pen sometimes has its cap on and then it's off again so you can see the blue tip.
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).
Revealing mistake: When Monica gets out of her room to show Chandler her sexy clothing, as she opens the room's door, the buildings from across the street move. The scenario was a curtain and the wind that the door made when she opened it on the set made those curtains with the buildings printed in move.
Continuity mistake: When Ross turns on the camera and sits down in front of it, "flirting" with it and drinking wine, what you can see on the little camera screen is very different from when they play the same clip on the TV, in which looks like he was sitting much closer to the camera then he actually was.
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.