Visible crew/equipment: Monica is talking to Pete in the diner when he gets back from Japan. If you look at the floor at Monica's end of the counter at the very beginning of the scene, you can see the mat that is there to protect her when she falls over later.
Continuity mistake: In The One With Monica's Boots, Monica is removing her trainers and replacing them with her boots so it looks as if she was wearing her boots all along. In one shot her left jean leg is tucked into her boots, but when she stands up it is sitting perfectly.
Continuity mistake: When Rachel wakes up Emma during a nap, against Phoebe's advice, there is a shot of Emma in the cot. She is wearing a plain pink hat, but in the next shot, when Rachel lifts her out of the cot, she is wearing a white hat with what looks like little flowers on it.
Visible crew/equipment: When Rachel is on the balcony with her date, after she kisses Ross and says, "Wow!", the shot changes back to her date. While he is saying, "Exactly" you can see a camera man on the left side of the screen. Then when the shot changes to show Rachel and her date you can see him move out of the shot.
Continuity mistake: When Phoebe says that they should not tell Ross that the date is cancelled so that he gets stood up, Joey says, "I hear that's bad" - implying that he has never been stood up so doesn't know how it feels. However, in TOW Two Parts (Part II), Ursula stands Joey up, and he takes it pretty bad.