Factual error: Phoebe discovers that one of the babies has wandered away, and finds the baby inside the open drawer. Yeah, no. These babies aren't even walking yet, much less are they able to lift themselves up past the height of their own bodies and launch themselves into a drawer.
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.
Factual error: The monkey is allowed outside his cage at an airport gate. Animals, with the exception of assistance dogs, cannot be transported in the cabin with passengers, and this rule applied in the 1990s as well. There is no way a monkey would be brought through a security checkpoint into a terminal concourse of a NYC airport and allowed aboard a regular commercial airliner.
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: When Ross shows Chandler the book, he claims it is in "the biggest library on campus" at NYU, which would be Bobst library on Washington Square Park South. Later, in Central Perk, when Ross tells Rachel and Joey about the people "making babies" in front of his book, Joey says, "Wait a minute. Fifth floor, against that back wall?" Bobst's fifth floor is conference rooms only; there are no stacks on that floor. Joey might have been confused, but Ross should know better, being a professor and having just visited that location.
Audio problem: Chandler, Monica and her parents are at dinner to discuss the upcoming wedding. When they describe how they remodeled the kitchen when she broke up with Richard, the camera pans to Monica and her mouth is moving but there's no sound. It then switches camera angles and Monica audibly asks, "Well what about when I started dating Chandler?" Which is what she said in the frame before with no sound.
Continuity mistake: When Rachel and Monica knock on Danny's door and he opens it, there is a wall a few feet behind him. Later, when Rachel shows up at Danny's apartment to cancel their date, she enters into an open room and there is no longer a wall in front of the door. Danny's apartment is supposed to be one floor directly below Chandler and Joey's apartment. This was obviously the same set for their apartment that was used for Danny's and the wall was added for that shot to disguise it.