Continuity mistake: In the opening scene Rachel is holding a white felt pen in her hands and gesturing with it while she talks about the soap opera digest magazine. Between shots the pen sometimes has its cap on and then it's off again so you can see the blue tip.
Revealing mistake: In the scene when they confront the stripper at Chandler's office. Ross stars shouting about his grandmothers ring, and as Chandler says "way to be cool, man", you can see Joey ducking behind Ross, covering his mouth with laughter. A brief cut away, then back and he's standing with the others again looking serious.
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).
Revealing mistake: When Monica gets out of her room to show Chandler her sexy clothing, as she opens the room's door, the buildings from across the street move. The scenario was a curtain and the wind that the door made when she opened it on the set made those curtains with the buildings printed in move.
Continuity mistake: When Ross turns on the camera and sits down in front of it, "flirting" with it and drinking wine, what you can see on the little camera screen is very different from when they play the same clip on the TV, in which looks like he was sitting much closer to the camera then he actually was.
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: When Joey walks back into the apartment (with his eyes covered) to get the sandwich, he walks by the Fussball-table, and there's nothing on it. When he walks away you see a purse lying on the cooker. Then, when the shot changes to Dina and Rachel, you see the purse lying on the fussball table.
Continuity mistake: In the opening scene where Rachel is checking the mail and is walking over to Monica's room, she has a pair of pumps on, then once she has walked in on Monica and Monica runs after her to say she was taking a nap, Rachel is wearing a pair of backless high-heeled sandals, then when Joey and Ross come in, Rachel is wearing the pumps again (we see this when Ross says "I had to talk loud because the movie was loud").