Continuity mistake: When they are talking about sperm donation, Joey is eating a cracker with jam on it. Between shots it instantly rotates in his hand. You can tell because the jam goes from being on the top to the bottom side, and because of the way he is holding it you can see there is only jam on one side.
Continuity mistake: When Chandler's boss is slapping all the guys on the butt, on the side of the table closest to the camera there is a tablet with a pen on it. When the guy comes back in to get his briefcase, the pen is no longer there.
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.
Visible crew/equipment: After Ross goes in for his disastrous tan, when it cuts to Joey and Rachel walking into their apartment the hole (used for a camera angle) in the wall can be seen at the right side of the screen. As an aside, when Ross leaves Monica and Chandler's apartment later just as Rachel walks in, that hole is seen in the hallway and it's covered up.
Continuity mistake: It's obviously December, with the set decorations and Rachel's reference to sitting on multiple Santas' laps because she is randy from her pregnancy hormones. The characters establish that it's Rachel's fourth month of pregnancy...but she became pregnant about six weeks before Monica and Chandler's May 15 wedding. Her fourth month would have been in July, not December.
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).
Continuity mistake: When Monica says, "I just recently got out of a serious relationship," she is holding her glass in her left hand. The camera cuts to Pete and the glass is now in her right hand. It then switches back to her left hand in the next wide shot.
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.