Continuity mistake: Right before Ross and Rachel storm in, the girls show Joey how much their waxing stuff hurts. Phoebe starts putting the wax on Joey's inner arm, but then the shot changes and she is spreading in on the outer side. Also she slaps the strip on and the blue tab is hanging down off his arm, but then the shot changes again and it is on his arm with the other end of the strip hanging off the other side.
Revealing mistake: When Monica offers Joey lemonade and he takes off his clothes and is behind the lamp, the tops of his boxer shorts are visible when he says "Were you just gonna give me lemonade?" Broadcasts may crop off this bottom part, DVD doesn't. You can also see his gray boxer shorts through the plant in the previous shot.
Visible crew/equipment: In the opening shot of Phoebe and Chandler in the "nine millionth" jewelry store looking for a ring, at the top of the screen we can see the tip of the boom mic moving in the wideshot. Then just as Chandler looks into the display case and says, "Ugly ring. Ugly ring. Ugly ring," the boom microphone can be seen moving around in the mirror's reflection behind him.
Visible crew/equipment: After Ross and Monica blurt out each other's secrets to their parents, when Jack says, "And we kind of figured about the porch swing," in his closeup we can see the end of the set wall, with the soundstage behind it and many tape marks on the floor.
Continuity mistake: After Joey makes up the story about how he slept with Monica once in London, in the shots facing Phoebe, Rachel, and Ross the door to Monica's apartment goes back and forth being either wide open or closed, depending on the angle of the shot.
Factual error: The restaurant refuses to take anyone's orders until they're all seated, which means that the group is sitting, occupying a table, without earning any revenue for the restaurant. There isn't a restaurant in NYC that would have such a policy, since it basically guarantees that a table becomes a revenue vacuum. (It also makes for very unhappy customers, but that doesn't qualify it as a factual error, since some restaurants might be actually stupid enough to not care about their return customers).
Visible crew/equipment: After Chandler starts removing Monica's braids from the shower curtain rings, when it cuts to Joey and Rachel walking into their apartment, we can see the hole in the wall at the right side of the screen. And it's seen again when Ross walks in on Rachel and Joey kissing.