While Joey is snooping in Pete's financial ledger, Rachel's torso and legs can be seen in the right-side corner of the screen. She moves her hands down near her thighs. Immediately after the camera angle switch (1 second), her hands are up near her chest again.
The second doctor who takes a look at Ross' thing brings two other people with him. A doctor would have to give a patient's consent before inviting other people as it is a HIPAA violation as the doctor would be at risk of either being sued or losing his job. Response: This was first broadcast in 1994. HIPAA did not effect until 2003.
When Ross goes to see Guru Saj, he has his "thing" removed. However, it is really obvious that Guru is not going anywhere near the thing, because you can see that Ross' shirt is still tucked into his trousers, and the Guru just rubs his hands along the shirt.
When the car catches fire you can see that the fire is not in the car but behind the car.
Ross' doctor tells him he can't have an extra nipple because it's located on his rear end. While most cases have the extra nipple somewhere on the torso, people can get them anywhere, even on an arm or a leg, so it is possible to have one where Ross' thing was located.
The doctor who takes a look at Ross' "third nipple" is incapable of putting on a rubber glove, even though he would have done so thousands of times during his 23-year career.
When the gang think Pete is going to propose to Monica, Rachel becomes excited and says Monica is going to marry a millionaire when Pete is actually a billionaire.
When Phoebe goes to break up with Vince, and when she opens his apartment door, Vince looks directly at the camera for a second.
When Joey is looking at Pete's bank book, he says millionaire when Pete is actually a billionaire.