The One With the Holiday Armadillo - S7-E10
Revealing mistake: When Ben sits on the sofa to listen to Ross talk about the festival of lights, you can see Monica move Ben to the other side of the sofa despite there being space for her to sit. This is so they sit in the correct order as she would mask Ben to the cameras.
The One With Ross and Monica's Cousin - S7-E19
Continuity mistake: When Monica comes into Phoebe's apartment for her Surprise Bridal Shower, the view of the hallway outside the apartment is a dead end on the right side (the left side cannot be seen), however, in S7:E12 (The One Where They're Up All Night), both when Phoebe is disposing of the fire alarm and when the fireman is at the door, it is clear that there is another apartment opposite hers, as well as a trash chute on the right side. (00:18:25)
The One With The Truth About London - S7-E16
Revealing mistake: When Monica gives Phoebe the headache medication (Hexadrin) she, not only doesn't take the lid off - and therefore fails in pretending to put it back on - but also doesn't actually give Phoebe anything. Extended episode. (00:07:30)
The One Where They're Up All Night - S7-E12
Revealing mistake: When Chandler is getting a pan out to warm some milk, he successfully pulls the bottom pan out without too much disruption, however, the joke (and entire plot device - to wake Monica up) is to make as much noise as possible so Perry pulls out more pans on purpose and knocks them on the floor. This is quite clear - you can see him grasp the wok and pull it out onto the floor. (00:06:30)
The One With Monica and Chandler's Wedding, Part 1 - S7-E23
Continuity mistake: When Monica and Chandler are talking about what his father might wear to the wedding, the door to their bedroom opens itself and then closes itself between shots.
The One With All The Cheesecakes - S7-E11
Continuity mistake: Just after Rachel has tried to whistle and just blew out crumbs, she picks up the fork with her left hand and places it to the left of the cake on the kitchen counter. In the next shot just before Chandler picks up the cake the fork is back on the right side of the cake near her right hand. (00:16:05)
The One With All The Candy - S7-E9
Visible crew/equipment: After Ross gives Phoebe the bike and she is leaving to ride it for the first time, the stage lights are visible in the rear view mirror.
The One With Ross's Library Book - S7-E7
Visible crew/equipment: When Ross says, "I work here," there is a stage light at the top to the right of Ross's head. (dvd)
The One With Ross's Library Book - S7-E7
Continuity mistake: When Chandler says "lie" his hand is by his side, then up. (00:07:20)
The One Where Chandler Doesn't Like Dogs - S7-E8
Continuity mistake: When Chandler is looking over Ross' list (right before he calls him Magellan), he has the front sheet of the paper folded up. In the next shot, the sheet is folded down.
The One With All The Candy - S7-E9
Continuity mistake: In the scene where Monica's female neighbour comes begging for candy, after Monica gives it to her and shuts the door it's a man standing at the door not the neighbour.
The One With Phoebe's Cookies - S7-E3
Visible crew/equipment: When Ross asks what do with all the cookies, a boom mic can be seen at the top of the frame. (Full-screen version only).
The One With Rachel's Assistant - S7-E4
Continuity mistake: Ross has always said that Carol was his first (and only, until Julie) sexual partner, but in the episode where they tell each others secrets Chandler says Ross slept with the cleaner when they were at college. Some people say that Ross had kept it a secret, and that's why it had never come out before, but considering that he categorically states several times over series one and two how he'd only EVER been with Carol, getting quite upset at times, that explanation just doesn't ring true.
The One Where They're Up All Night - S7-E12
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. (00:02:20)
The One Where Rosita Dies - S7-E13
Continuity mistake: When Chandler and Rachel figure out that the chairs were switched they both head over to Joey's apartment. When they 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. (00:20:05)
The One With Monica's Thunder - S7-E1
Continuity mistake: When Rachel and Ross go to talk to Monica about why she doesn't want to talk to her, Chandler's tie changes, from on the bed to on his lap.
The One With The Truth About London - S7-E16
Visible crew/equipment: As Joey is entering Monica and Chandler's apartment, there is a black microphone visible for a few seconds moving above Joey's head as he is walking towards Monica and Chandler at the table.
The One Where They All Turn Thirty - S7-E14
Plot hole: There's no way Phoebe has lived to 31 without knowing her birth date. She's had "real" jobs (like the massage parlor) and those require social security numbers and accurate birth dates. She didn't go to high school, but she mentions classmates, so she must have gone to elementary/middle school, and those required birth dates even in the '70s and '80s. She's also "lived in Prague," which she couldn't have visited without a passport - which requires a birth certificate.
The One With Ross's Library Book - S7-E7
Continuity mistake: When Monica says, "she's not going to like that chicken either," Chandler's arms are crossed. Then the shot changes, and they're now by his face. (00:07:50)
The One With Monica's Thunder - S7-E1
Visible crew/equipment: When Monica says she's opened the door to the past, a little bit of a stage light is visible above her head.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.