Continuity mistake: When Chandler is sitting in his kitchen with Monica and Phoebe, talking to the woman on his computer, the camera is on Monica, showing part of the computer screen. The screen is blank, indicating that the computer is off. In the next shot, the sound of an instant message is heard, indicating that the computer is in fact on.
Continuity mistake: When Chandler's in Rachel's office, she tells him the lingerie isn't kept there. He says, "Yes I realise that", and starts reaching for the catalogue she's about to give him. Camera cuts, and he's now standing with his hands in his pockets, reaching out again when she gives him the catalogue.
Continuity mistake: Chandler is able to get into Monica's apartment to tell everyone that Underdog got away, but later when Rachel closes the door it is now locked. We can see the door as each person is leaving and nobody does anything which could be construed as locking the door before it closes. It's been often demonstrated in the show that the door doesn't lock automatically.
Continuity mistake: When the friends are talking about the contest to prove who knows each other better, Monica says to Joey "Are you scared?" and Rachel has her arms crossed. Joey says "No" and in the next shot of Rachel she is crossing them again.
Audio problem: When Joey is proposing to Rachel and he tells Phoebe to give him the ring back, she says "No!" and pulls her hand away. When she pulls it away, she hits her chest and there's a thump sound that's clearly the sound of her clip on microphone being hit (it's way too audible to be just a thump on her chest).
Visible crew/equipment: In the scene where Phoebe knocks over the vase, after she says, "Well, that's just the way things go" and turns around to face the babies again, you can see a crew member coming out of Rachel's room. When Phoebe starts looking for the missing baby, the shadow of the crew member is visible on the right of the screen as the baby is placed in the drawer.
Continuity mistake: At the end when Chandler is singing "Endless Love", Phoebe comes in and when she walks over to Chandler he has his arms wrapped around the Lionel Richie record with the shoe in his hand in front of the record. When the shot switches to just Chandler, his right arm is resting on the arm of the chair and his left arm is holding the shoe behind the record.
Continuity mistake: Phoebe is complaining about people disrespecting her charity bucket, and hands the bucket to Monica as she does so. In the first two shots Monica holds the bucket by its edge, but when the camera goes back to her for a third time, she is holding the bucket by its handle.
Continuity mistake: There is a shot of Phoebe in Central Perk about to talk to Frank (from outside, looking in). From this shot there are several people outside Central Perk. The camera does an instant cut to behind Phoebe, (inside, looking outside) and the people have vanished.
Continuity mistake: Phoebe and Ross are in the soon to be closed bar sitting on the pool table. He clears it of everything, but a few seconds later he stops making out because the "damn balls are in the way" and somehow magics up a handful of snooker balls. If you look closely when he's clearing the table, there are two dark balls at the side which he studiously ignores, and which Lisa Kudrow then surreptitiously grabs and takes onto the table with her so David Schwimmer can grab them later.
Continuity mistake: Chandler walks into his apartment to find Rachel eating cheesecake without him. As the door is shutting, the pen on the Magnadoodle is hanging loose; it can be heard hitting the door when Chandler is closing it. The next shot shows Rachel stop eating, and when we next see Chandler, the door is closed and the pen is in its holder.
Revealing mistake: When Joey has the turkey on his head, and Chandler is by the door, look at the wall to Chandler's right. It's a "wild wall" - i.e., a movable wall put there to extend the set outward an additional few feet, since the camera normally doesn't see that far forward. The wall angles oddly away from the room, and you can see how the line and pattern of the hallway floor continues into the room.