Character mistake: The officers count the inmates and say there's 10 missing. There are indeed 10 inmates hiding in the pool. However, Pennsatucky and Chang had escaped the prison. The officers counted Linda as an inmate, who had been hiding in Litchfield the whole season, and wasn't on the list. That would make it 11 people missing, not 10.
Continuity mistake: Maria branded Piper on her left arm in season 4. In this episode, the scar is on Piper's right arm.
Factual error: Tiffany asks a guard where he would go if he could travel back in time. He says he would return to 1999 to attend a Judas Priest concert he missed. He says he wasn't able to get close to Rob Halford. The problem is Rob Halford was not the lead singer of Judas Priest in 1999. Tim 'Ripper' Owens was.
Continuity mistake: In season 3 Baxter Bayley's uniform reads C. Bayley. In season 4 it reads B. Bayley.
Character mistake: At the end of the episode when Maria is framed for the prison panty business and told to expect an additional 3-5 years on her sentence she cries saying that her daughter Pepa will be in kindergarten by the time she gets out. However in season 2 episode 12 Maria tells Piper that she still has 6 years left on her sentence. This means that even without the extended sentence her baby would have been well past kindergarten age by the time she was released, so taking the extra 3-5 years into account, Pepa could be almost finished in elementary school by the time her mother got out of prison.
Blood Donut - S1-E7
Visible crew/equipment: When Flores discovers her cell phone is missing from the hole in the wall she goes nuts, slams the stall door and kicks it in. After she is taken away there's a closeup of the stall and we can see the metal spring that was duct-taped to the bottom of the wall inside.
Continuity mistake: When Piper confronts Alex in the bathroom (saying "you named me"), When Alex turns away you can see that her salt shaker tattoo is upside down.
Moscow Mule - S1-E8
Continuity mistake: Mercy, who was released several episodes earlier, can be seen sitting at the table when Maria comes back in.
Continuity mistake: In season 5, CO McCullough mentions that her first name is Artesian. However, in season 6 her uniform says her name is B. McCullough.
Continuity mistake: Near the beginning, Piper is sitting on the toilet and you can see her new engagement ring on her finger. When she wipes her eyes with the tissues the ring has vanished. A couple of shots later the ring is back.
Chocolate Chip Nookie - S6-E10
Continuity mistake: When the officer is taking Gloria to D-Block because she had a "friend in high places," and she asked where he was taking her, when she's walking down the hall towards D-Block, she's only carrying a small bundle of belongings, but then once it cuts to her entering D-Block, she's now carrying all of her stuff in a much larger bundle. (00:44:00)
Lesbian Request Denied - S1-E3
Continuity mistake: Larry and Cal are cooking hot dogs over an open fire. Larry starts out with a straight stick, Cal with a curved stick. Larry puts his hotdog on the curved stick, then has the straight stick as he puts it over the fire. The swap happens again and Larry ends the scene with the curved stick. Also, the tip of the straight stick swaps from a sharp point to a dull point. (00:40:30 - 00:41:50)
Blood Donut - S1-E7
Continuity mistake: When the girl is holding the flash light to her face, the next shot it's the other way around, then a couple of seconds later it's the first way again. (00:14:40)
Continuity mistake: We see Sophia's long hair from the side as we watch Red and Mendoza talking. A minute later, we turn back to see her face and she has a short shoulder length haircut. (00:48:10)
Factual error: Whenever Tiffany gets her dentures there's one problem. She's got her hands cuffed in front and prisoners, unless they're cuffed to the waist and ankles too, should have her hands cuffed behind her back.
Full Bush, Half Snickers - S5-E7
Continuity mistake: When Red and Flores are texting Piscatella to come into the prison from Humps' phone, in one of the texts, Humps says "Thx" and Piscatella texts "Np". The time Red and Flores send is 4:59 and the text is sent from iMessage. When Piscatella checks his phone the time is 4:56, the messages were sent by the opposite people, and it's an Android phone, incompatible with iMessage. (00:53:03)
Continuity mistake: During episode 6-3, it is established that all inmates at the Ohio prison facility are required to have their hair cut in order to prevent the spreading of lice. Later on in the series, it is revealed that almost all of the inmates that were not moved to Litchfield Max after the riot were sent to Ohio. Despite that, several of the inmates formerly from Litchfield were shown still having long hair in scenes that took place in the Ohio facility, and Maritza's hair was long when she first appeared at the nightclub while she was on parole. While it is possible that the policy may have been rescinded between the events of seasons six and seven (which would explain why Alex's hair was still long when Piper visited her), that does not explain the other characters that were immediately transferred to Ohio still having their hair long during subsequent appearances.
Character mistake: The zip tie handcuffs on the arrested inmates were not tightened. (00:25:18)
Other mistake: The subtitles refer to the men cheering for the female soldier that was stripping as "Marines" despite all of them being in the Army. (00:24:10)
Plot hole: "Red" is somehow serving a life term or what for the execution murders of some Russian spies, her husband and his cronies had headed up. But her hubby somehow escaped any such sentencing.
Answer: You would need to be more specific as to which inmate to get an answer as to who possibly belongs in the mental ward. In general; usually the only mentally ill prisoners who go to the mental ward are inmates who show obvious psychotic breaks like Loli and crazy eyes as, with the conditions of prison, it's often difficult to tell who is mentally ill and whose frustrated from the conditions. Many of them are also only there temporarily. Crazy Eyes, first example, was in the mental ward. Her mother fought and won to get her out.