Continuity mistake: When Chandler and Rachel figure out that the chairs were switched they both head over to Joey's apartment. When thet enter the apartment, the new black chair can be seen with tags attached to the top and left side. When the scene cuts to Joey sitting down the tags are all missing from the chair.
Plot hole: David Schwimmer is 6'2" tall and Jennifer Aniston is 5'6". There is no way that clothes that fit Rachel would also fit Ross. When he puts on the clothes that Rachel bought it's obviously not Rachel's size. If it really were, it would be a lot tighter and shorter (Ross could probably wear it belly free).
Continuity mistake: Apparently Ross is Monica's older brother but in "The one where they're going to party", Joey states that the three men are all the same age ("we're 29, we're not women"), and in the one with the birth Monica says she is 26 and Joey says he is 25. If Joey is younger than Monica, and Ross and Joey are the same age, then there's definitely a mistake somewhere.
Plot hole: It is made clear through dialogue in the episode that Joey and Ross are stuck on the roof because Joey removed the bit of piping holding the door open. However, when Tag, Rachel and Phoebe get up to leave, Phoebe says "Shh, get me out of here" and there is a clear shot of the door standing wide open. Afterward, it is possible to see Tag reaching for the door handle to close it behind him. This is inconsistent with the idea that the door needs to be held open.
Continuity mistake: Chandler, Monica and Phoebe are shown listening at the wall between their room and the room Ross is in with Charlie. However, when Ross comes into the room, the outside hallway is shown, and it is clear that the wall they were listening at actually connects to the hallway, not another room. Ross even walks in that direction when he leaves, proving it's not a dead end or similar.
Continuity mistake: In the scene where Chandler turns on music when he and Phoebe are going to "have all the sex" you see Phoebe's arm begin to move in the right corner of the screen. When it cuts to her she has not yet begun dancing, and when he goes to turn the music on again it is a duplicate clip from the initial shot.
Factual error: There is an impossibility with the hotel rooms in Barbados. Ross gets from Monica and Chandler's room to Rachel's room far too quickly for it to be real. Also, when the camera moves between rooms (cutting through the wall), you can see that both Rachel and Ross' rooms are too long. If the walls were where they actually are, they would edge through into Monica and Chandler's room.
Continuity mistake: When Ross and Chandler are talking about who broke which pact in college (the girls they agreed not to date) they are standing at the drinks table. Chandler is holding a drink in his left hand and his right hand is in his pants pocket. The shot then changes to face Ross, Chandler does not remove his hand from his pocket, but in the next shot facing him his drink is in his right hand. He then places it on the table.
Continuity mistake: When Monica's mum and dad are leaving the party, they are standing next to each other while her dad explains why he can not drive anymore. Her mum has both hands in front of her holding on to her purse, in the next shot one arm is around Monica.
Factual error: Phoebe discovers that one of the babies has wandered away, and finds the baby inside the open drawer. Yeah, no. These babies aren't even walking yet, much less are they able to lift themselves up past the height of their own bodies and launch themselves into a drawer.
Continuity mistake: When Phoebe, Chandler, Monica, and Joey are eating the organic wax, Monica has her feet up on the wall with her legs crossed left over right, but in Joey's closeups when he asks about needing a new walk, Monica's legs are crossed right over left.
Factual error: This show is set in October (it's a Halloween party). Rachel's stomach is completely flat, but according to the show, she got pregnant in April (It's stated several times by the characters on the show that Monica and Chandler's wedding was in May, and we learn in "The One With the Red Sweater" that she got pregnant a month before the wedding. Hence, April). However, by October she should have a six months' pregnant belly, which is no way resembles the perfectly flat belly she shows.
Character mistake: After the guys have beaten the girls in the quiz, Rachel refuses to move apartments and Monica says: "If we had lost, we would have made them get rid of the birds." But they did lose. That's why the guys have got their apartment. She should have said if we had won.
Continuity mistake: After Phoebe tells Monica that she is fired from being her wedding planner, Monica says that she has never been fired. However, in "The One with Five Steaks and an Eggplant" Monica gets fired for taking the kickbacks.