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.
Other mistake: When Ross is helping choose a dress and shoes for Nana to wear, he is behind the chest of drawers in the cupboard. He looks in a shoebox and finds lots of pink sweet'n low packets, then pulls down another box and lots of packets fall down on him. However, it is obvious that someone is above him showering the packets down, as they are coming from directly above him, not from on top of the door.
Continuity mistake: When they are in the coffee house talking about the fact that Joey missed his audition, Phoebe says, "And that is why we don't invite you to play." Her hands are at chest height, but in the zoomed out shot, they are lowered.
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.
Continuity mistake: The position of the lid of Janice's box of contact paper changes repeatedly and after she tells Chandler she doesn't know what to say, she begins to slide the roll of paper back into the box. In the shot from behind, the box is closed.
Continuity mistake: There is a scene in the guys' apartment where the phrase on the Magna Doodle keeps changing. Joey is complaining to Chandler about having to stay awake all night for a sleep study. Rachel and Ross then enter the apartment (at different times) and Ross announces he is getting married to Emily in a month. In some shots during the scene the Magna Doodle reads, "get out!" in other shots it reads, "Poop." (Widescreen).
Continuity mistake: At the end of this episode, Ross enters the door of Joey's apartment and finds Rachel and Joey kissing. Rachel says "I'm so sorry". The next episode, The One When Ross Is Fine, shows the same scene but it has been changed: Rachel never says "I'm so sorry". Joey starts talking when Ross enters the room.