Continuity mistake: In the one with Rachel's new dress, she's in her underwear on the sofa when Joshua comes in. In wide shots focusing on Joshua she's quite laid back, but in close shots of her she's sitting more upright. Worse than that, her legs are crossed, but uncross in the shot of his parents coming in, only to re-cross in the next shot when she gasps.
Continuity mistake: At the rehearsal dinner when Chandler loosens his tie and unbuttons his collar, the tie changes its appearance in the following shots from being tighter to looser several times.
Continuity mistake: When Monica comes round to Phoebe's, Phoebe reminds her that she's got to clear out stuff. In this wide shot Monica has both hands by her sides, but when it cuts to her finishing saying "oh right", her right hand is now gripping her bag's strap.
Continuity mistake: Ross, Joey and Chandler are in Chandler and Joey's appartment talking about Ross' decision. Chandler has a green bottle in his hand. He puts it down behind the computer by the microwave, but when Ross starts listing Rachel's "cons" the bottle's suddenly at the opposite end of the counter.
Continuity mistake: When Ross gives the super the money and asks "will this help with the knob" the super says that the place isn't open until Tuesday. When he says that the money is in his right hand. Then when he asks "am I not saying it right", the money in his right hand is gone.
Continuity mistake: When Mike says "I am going to make this decision for us. What do you think we should do?" he is holding the check. The very next shot shows the charity worker taking the check off the desk and giving it back even though Mike never put it down.
Character mistake: Ross tells Chandler to run a "post pattern to the left." (And Chandler quickly agrees.) In football, this is a type of passing play where Ross would hold on to the ball while Chandler runs straight down the field immediately after the snap, eventually veering diagonally to the left once he's a ways down field to receive a pass from Ross. The play that they actually run is completely different. It's a running play known as a sweep. (A toss sweep to be precise.) There is no possible way that anyone either making play calls or running them would ever confuse a post vs. a sweep.
Deliberate mistake: The door to Monica's bedroom is open in many shots, such as when Ross introduces Julie, and we can see that there's a wall (with a framed picture) directly opposite the doorway, but when Phoebe's giving Monica the haircut they're in Monica's bedroom and there's no such wall in front of the door.
Other mistake: After Rachel takes the phone from Ross and hangs up on Julie, when she's sitting at the table there's a bottle of Evian water in front of Monica with part of its brand name covered - the letters "e" and "n" are whited out leaving "via" on the bottle.
Factual error: Phoebe holds up a bag of quarters that is almost the size of her head. This would be physically impossible for anyone except perhaps the world's strongest weight-lifters. Quarters are exceptionally heavy for their size. Two rolls weigh exactly a pound. It would take at least 300-400 rolls worth of quarters to fill up the bag Phoebe is holding, which means she is lifting 150-200+ pounds, primarily with one arm.