Continuity mistake: In Central Perk, when Phoebe writes a note for Ross to put on his sandwich so no one eats it, she mentions that she stabbed a cop, and has a green mug in her hand. It cuts to Monica then back to Phoebe and the mug is out of her hand and she's yelling, "He stabbed me first." When it cuts back to the wide shot the mug is back in Phoebe's hand.
Continuity mistake: After Rachel and Phoebe see Bonnie and Ross in Central Perk, Rachel is yelling at Phoebe that she needs to break them up. At first, Phoebe is holding her coat in her left hand and a purse in her right, but then she is holding them both in her left, with no time to have changed hands.
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: 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.