Factual error: This mistake is from series 6 onwards, with Ross' new apartment: There is an impossibility with Ross' kitchen, but not all of the time. It depends on the layout of the hallway outside his apartment. If the hallway continues along for a bit before going left or right, then the kitchen should stick out. However, when the hallway is a dead end, the kitchen fits ok.
Continuity mistake: The white dog that Joey gives Chandler sometimes has red lips and sometimes does not.
Audio problem: Right after Ross and Rachel leave the wedding chapel, Joey and Phoebe rush in. Joey is saying "C'mon, Pheebs, hurry, hurry." and she is saying "Okay, okay." However, neither one is moving their lips. (00:00:25)
Continuity mistake: In the previous episode, Ross rings the helpline of the makers of the pen and is told the pen won't come off. Yet in this episode it vanishes from Ross and Rachel's faces between getting up and going to breakfast. (00:02:25)
Continuity mistake: When Ross and Rachel are in bed, and Rachel says she remembers laughing a lot, and Ross says "Then we didn't have sex," Rachel turns her head away from Ross twice. (00:03:10)
Continuity mistake: During breakfast, when Joey and Phoebe are talking about driving back, the fork in Phoebe's left hand disappears and reappears. (00:03:55)
Continuity mistake: Joey's Hand moves from putting it to his mouth to the plate instantly at breakfast. (00:06:35)
Revealing mistake: When Joey and Phoebe are driving back, the outside is obviously a projection. (00:10:15)
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)
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 Hugs Rachel - S6-E2
Continuity mistake: In the scene where Rachel is all happy that the three of them are going to live together, her arms keep changing position throughout the scene. (00:08:35)
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 Ross Hugs Rachel - S6-E2
Other mistake: When Monica's trying to evoke some kind of an emotional reaction from Rachel, who's polishing her toenails, there's a bottle of Cutex nail polish remover on the table with part of the brand name painted black, so it reads "Cu Ex" on the label.
The One Where Ross Hugs Rachel - S6-E2
Other mistake: In this episode, Chandler says that "when it comes to sweets, [Joey] is surprisingly strict" and doesn't allow sweets around the house. Except that in Season Five, "The One With The Kips," we see that Joey leaves Rollo candies everywhere.
The One Where Ross Hugs Rachel - S6-E2
Audio problem: In the pre-theme-song scene, with Phoebe and Ross talking outside the coffeehouse, when Phoebe sends Rachel away in the cab for the second time the sound of the tyres screeching starts while the cab is still stationary.
The One With Ross's Denial - S6-E3
Continuity mistake: When Monica and Chandler are eating, Monica's plate holds a sandwich and chips. When Joey comes in, Monica's plate contains no chips, and when he leaves the chips are back again. (00:04:00)
The One With Ross's Denial - S6-E3
Continuity mistake: When Joey is interviewing the potential roommate and Chandler comes in, Joey's stance changes a few times. His grip on the application form changes, and when he points to the bathroom his arm is in a slightly, but noticeably, different place in the next shot. (00:11:10)
The One With Ross's Denial - S6-E3
Visible crew/equipment: After Ross tells Rachel about Warren's apartment he gives her Warren's phone number, and in the closeup while Rachel hugs Ross, and also in the following wideshots which face Ross the camera can be seen at the right side of the screen.
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.
The One With Joey's Porsche - S6-E5
Visible crew/equipment: Anytime we see the Porsche, there is always a stage light above it. (00:03:30)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.