The One With The Proposal, part 1 - S6-E24
Factual error: There's no charity event in the world that would be clamoring for non-paying guests and offering them free food and an open bar.
The One With The Apothecary Table - S6-E11
Visible crew/equipment: After Rachel tells Ross that Phoebe hates Pottery Barn, when she tells him that Phoebe will be there any second and they need to cover the apothecary table, a crew member can be seen at the left side of the screen.
The One Where Ross Dates a Student - S6-E18
Continuity mistake: In the dinner scene between Chandler and the girl from college, the spoon in front of Chandler moves without him touching it. (00:13:45)
The One With The Joke - S6-E12
Continuity mistake: At the end Rachel turns away from Gunther and pulls her sleeves above her elbows. Next shot they are below her elbows. (00:20:00)
The One With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: When Chandler answers Joey's phone there is a drawing on the magnadoodle. However in the next shot it has vanished with no time. (00:17:20)
The One Where Ross Got High - S6-E9
Factual error: A really picky one: When Ross looks at the recipe book, he says Rachel's made 'half a Shepherd's Pie'. Technically, a Shepherd's Pie is made with lamb, whilst it's a Cottage Pie that's made with beef (although the two names are often interchanged).
The One With The Apothecary Table - S6-E11
Continuity mistake: When Chandler says "Oh, just like the apothecary table of yore," Monica turns her head toward him twice. (00:02:30)
Factual error: The makeup on Rachel's face "can't be covered up with makeup," and "won't come off," we learn in The One In Vegas, Part 2. So it's not a surprise that she still wakes up with it on (and so does Ross.) but an hour or so later, when she's at breakfast, it's not there. An hour or two won't make the magical difference that 8+ hours didn't.
The One Where Ross Got High - S6-E9
Plot hole: Monica is trusting Rachel to make a traditional English trifle and being a top chef (or an even averagely intelligent human being) she would know what ingredients are used in one. So there's no way she could have missed Rachel cooking beef with peas and onions during the cooking process. Rachel's cooking it right there in Monica's kitchen while everyone else is there!
The One With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: In the episode before, Rachel's hair is just underneath her shoulders. Then, a few weeks later when Ross gets back from Spring Break, it's a lot longer than before.
The One With The Apothecary Table - S6-E11
Audio problem: When Phoebe puts her feet up on Ross' apothecary table, Ross asks her not to put her feet up on his "new...old sheet." During the pause right after he says "new," there's a cut to a different angle and you can see his mouth form the words "old sheet." Then it cuts to a different angle and we actually see and hear Ross say "old sheet." (00:12:05)
The One Where Joey Loses His Insurance - S6-E4
Visible crew/equipment: After Rachel speaks with an Indian accent and comments on Bombay, it cuts to an exterior shot of Central Perk and inside we can see the top of the set, as well as a lighting rig at the ceiling.
Continuity mistake: When Joey and Chandler talk about how to tell Monica that it is too soon for marriage, Joey fills his plate up with scrambled eggs. When he walks over and sits at the table, the eggs appear smaller on his plate. (00:15:54)
The One Where Ross Hugs Rachel - S6-E2
Visible crew/equipment: After Ross tells Phoebe that he does not have feelings for Rachel, just as Ross walks into the apartment to find Rachel crying, the shadow of the moving boom mic can be seen on the wall at the top, left side of the screen. (00:20:15)
The One Where Chandler Can't Cry - S6-E14
Continuity mistake: In the beginning of the episode when Joey tells Chandler that he hasn't forgiven him for kissing one of his sisters, Monica and Chandler's TV, entertainment set and ferns are missing from the set and there are cables protruding from the wall. The area is completely bare except for the French poster. Everything's back to normal slightly later in the episode.
The One Where Paul's The Man - S6-E22
Continuity mistake: In the opening scene in Central Perk when Paul (Elizabeth's dad) takes Ross to one side to talk to him you can see the girl in the blue top enters the door twice: first the shot after Paul says "I'm funny like that" and then again after Ross says "I realise it upsets you".
The One With Mac & C.H.E.E.S.E. - S6-E20
Plot hole: When Chandler is in Joey's apartment, he answers the phone and says, "Joey's not here right now, can I take a message?" A split-second later, we hear Chandler say, "Yeah, so the audition's been moved from 5:00 to 2:30?" It would be 100% impossible, within the fraction of a second that Chandler is silent, for the other party to pass along the fact that Joey's audition has been moved and the new start time. In fact, there wouldn't have been time to speak more than a couple of syllables. (00:08:45)
The One Where Ross Dates a Student - S6-E18
Other mistake: Ross' semester supposedly just ended, and he's handing in his grades. But the episode just before this one was about Valentine's Day, and the one immediately after this one is about spring break, so this episode is happening sometime between mid - February and March/April. It doesn't matter when the show was aired or produced; Valentine's day is still in February. There's no semester that ends at that time of the year, and NYU wasn't on the quarter system then.
Suggested correction: This episode (production code 225567) was produced before episode 17, "The One With Unagi", (production code 225568) and just aired out of order. So this episode happens before Valentine's Day.
The One Where Ross Got High - S6-E9
Continuity mistake: When Rachel tells Phoebe that she's making a traditional English trifle, Monica's holding a cloth napkin, but in the next shot the napkin's suddenly gone and she's now holding forks.
The One Where Ross Got High - S6-E9
Continuity mistake: When Phoebe finishes telling Rachel about her thanksgiving dream about Jack, Chandler is looking straight ahead with his arms crossed. Cut to the next shot when Jack and Judy are coming out of Monica and Chandler's room, and his arms are immediately uncrossed and he's looking at the women. (00:20:05)