Continuity mistake: In the scene where the gang is watching Joey's "substitution" video, you can easily see the reflection on the television that no one is sitting on the couch, but when the camera goes back to the gang, they're sitting down on the couch.
Continuity mistake: When Phoebe and Rachel are first talking about the apothecary table, there are two piles of CDs on it. In the side shot you can see that the two CDs on the top of the pile in front of Rachel are overhanging by a few centimetres. A few shots later, however, the top two CDs are overhanging on a different side.
Continuity mistake: After Phoebe tells Monica that she is fired from being her wedding planner, Monica says that she has never been fired. However, in "The One with Five Steaks and an Eggplant" Monica gets fired for taking the kickbacks.
Continuity mistake: When Phoebe and Ross are talking about Ross buying his sheets at the flea market, Phoebe says, "Ross, come on, you gotta loosen the purse strings a little" with her hands by her side. The camera cuts and her hands are now out in front of her.
Continuity mistake: When Paul the Wine Guy first comes to Monica's apartment, Phoebe is standing in the kitchen telling Rachel that she just pulled out four eyelashes. But in the very next shot, you can see her sitting in an armchair in the living room. [Broadcast version only - in the extended DVD version there's a shot showing Phoebe walking to the chair.]
Visible crew/equipment: Right after Rachel says, "Do you know that feeling when you're trying to blow a Saint Bernard out your ass?" the camera cuts to a view of Monica and Chandler. Behind Monica and Chandler, part of the set is visible, along with a man on crutches.
Plot hole: In the opening scene Phoebe and Chandler discuss how Phoebe knows Chandler is going to propose: by walking in on him whilst he was looking at a ring catalogue on the toilet. However, in the previous episode Chandler leaves the apartment right after he found out about Monica booking the wedding slot (on the answerphone) and doesn't come back until he 'freaks out' at Monica and then it is revealed that it was just put on and Phoebe is in on the plan. It doesn't add up, as Chandler would have had to have been looking at the catalogue between hearing the message and deciding to propose, in the same afternoon when he wasn't even in the apartment.
Factual error: The guys are gone for a single night, watching the Knicks game. (You can tell this because they talk about how "we can go see the game tonight," and when they get back everyone's wearing the same clothes as that conversation.) When they get back, both apartments are completely switched back: the large, heavy furniture is replaced, the posters are re-hung, etc. Even if they were gone from, say, 6 p.m. to midnight or so, there is no way that Rachel and Monica would be able to make that transition in that kind of time.