Continuity mistake: In the flashback where Joey sticks the turkey on his head, the subtitle says Thanksgiving 1992. However, the show started in 1994 and Joey didn't move in until the previous fall, so the earliest Thanksgiving that he was there would have been 1993.
Continuity mistake: In the scene just before Joey goes into the shower, when he is thanking the director for the opportunity, the camera shot goes back and forth between Joey and the director several times. During this series of shots, the part in Joey's hair switches sides nearly every time. It appears that the entire shot is reversed - in the closeup, the shower curtain is on his left and the shadow to his right is sharply focused. In the lower (long) shot, the curtain is to his right, and the shadow on his left is more focused.
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: Towards the end, during a scene at Ross and Rachel's, Sandy picks up two puppets and puts them on each hand. He starts pulling the blue one onto his left hand, but when the angle changes there's a yellow one on his left hand, and a blue one on his right. It cuts to Ross, then when we go back to Sandy they've changed hands again.
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: During the scene when Phoebe breaks into the other Phoebe's house and gets caught, the older Phoebe was telling the younger one that the man in the photo is not Frank Buffay, but is Chuck Mangioni. Right after that, as Phoebe 2 walks towards the camera, you can see that the door behind her moves open, and there is a visible shadow of someone who walks by that doorway.
Character mistake: When Monica and Mike are playing table tennis, Monica puts her hand on the table and looses the point. Mike then does the same thing. Surely Monica, of all people would notice that as it would have given her the point. We also see her looking at Mike at the time.