Visible crew/equipment: When Rachel opens the door to the apartment while she's holding flowers and sees Phoebe trying to get up from the couch (before the wedgie comment), the open edge of the set wall can be seen at the top left corner of the screen.
Factual error: Phoebe holds up a bag of quarters that is almost the size of her head. This would be physically impossible for anyone except perhaps the world's strongest weight-lifters. Quarters are exceptionally heavy for their size. Two rolls weigh exactly a pound. It would take at least 300-400 rolls worth of quarters to fill up the bag Phoebe is holding, which means she is lifting 150-200+ pounds, primarily with one arm. (00:08:40)
Revealing mistake: In the scene where Chandler confronts Janice about Joey seeing her kissing her ex-husband, Janice begins to hyperventilate. However, right before Chandler gives her the paper bag, Janice spins around and places the receipt in her mouth. Conveniently, after she begins breathing into the bag, she "chokes" on a receipt. (00:10:07)
Plot hole: This is actually for both parts of "The One in Barbados": it's shown that Monica's hair gets all frizzy from the humidity. And yet she's shown all throughout with her hair out and loose in all its frizzy glory, though it bugs her. I could maybe buy that not one of the women have hair gel with her (not bloody likely.) or that the fancy hotel doesn't sell hair gel (possible). But resourceful Monica would have thought of something to calm down her hair, or she would have just tied it up in a ponytail or bun - she does care a lot about her appearance. It makes no sense other than for comic value. (00:09:30)
Continuity mistake: Just after Rachel throws a bread roll at Joey, he turns to Chandler to speak to him. Chandler is holding his hands out in front of him. In the next shot, his right hand is touching his face, then in the next shot, it is lowered again. (00:02:55)
Continuity mistake: In this episode, Rachel tells Chandler that she thought he was gay until he spent Phoebe's entire birthday party talking to her breasts. But at this point since Rachel joined the group, Phoebe hasn't had a birthday yet; that occurs some episodes later, in "The One With Two Parts." (00:02:00)