Visible crew/equipment: While Phoebe and Rachel are with Monica in the guestroom, Phoebe decides that Rachel should be the one to get the nice room, and right before Monica tells Rachel that she's the first guest at "Hotel Monica" we can see the end of the bedroom set wall, with the kitchen and living room visible.
Continuity mistake: When Monica is standing in front of Phoebe, asking if the smell from Joey's is bothering her, the shots of Monica from the front show her arms held out in front of her, but when the shot changes her arms are crossed. This happens twice. (00:11:15)
Continuity mistake: When Rachel and Joey are at Joey's apartment throwing wet paper towels at the entertainment unit, Phoebe comes in to ask Rachel to switch back to Monica's apartment. During the scene, Phoebe is standing in front of the entertainment unit, and the wet paper towels' number and positions change between shots. (00:18:10)
Other mistake: Ross' semester supposedly just ended, and he's handing in his grades. But the episode just before this one was about Valentine's Day, and the one immediately after this one is about spring break, so this episode is happening sometime between mid - February and March/April. It doesn't matter when the show was aired or produced; Valentine's day is still in February. There's no semester that ends at that time of the year, and NYU wasn't on the quarter system then.