Mosley Lane - S5-E16
Character mistake: Reid tells Mrs. Hillridge that he's been working for the BAU about five and a half years, which is roughly since the pilot aired in 2005. But flashbacks in "Tabula Rasa" show that Reid was a relatively new rookie in 2004, which is roughly six years. Considering Reid has an eidetic memory, the six-month discrepancy is a bit suspicious.
Character mistake: In this episode the unsub is copying the murders of Jack the Ripper (with men as victims). The Unsub also taunts the police and BAU with letters, even using the Dear Boss salutation. The BAU draw upon the Dear Boss letters from the original Ripper case as part of their profiling - not only of the unsub but also the Ripper. Handwriting comparisons has shown that the author of the Dear Boss letters was most likely a journalist and not the Ripper. Whilst the unsub may have been ignorant of the forgery status of the dear boss letters, you would expect the BAU to be wiser.
Revealing mistake: When Hotch and Spencer are interrogating Eddie, Spencer shows him the three photos of the people he has killed. Eddie makes a gesture as if to speak and points at Spencer, at which point we see a shot of Spencer and he very obviously glances into the camera.
Character mistake: When Reid realizes who the unsub is, he asks Hotch if he was introduced as "Doctor" or "Agent". As explained in the pilot (and in every episode since), the team has always introduced Reid as "Doctor", to make sure that the people they meet treat him with respect and don't just see him as a kid.
Suggested correction: I think the reason Reid asks for a clarification is because the unsub knew his name and title when he hadn't been formally introduced because this case was under special circumstances so the team wasn't being formal.
It has nothing to do with being formal. The mistake is saying the team never introduces Reid as "Agent Reid", so there's no reason to for Reid to even ask this question.
I think what they meant was that it would be assumed his title was agent, as he is a part of the FBI, but she addressed him by his correct title without any indication of his title being different to the others, which ultimately suggested that she knew Reid beforehand.
Plain Sight - S1-E4
Continuity mistake: At the very end on the plane, Gideon gives Reid the two tickets as his birthday present. In the shot facing Reid, he holds the tickets facing himself. In the reverse shot, the tickets now face Gideon. (00:39:30)
Demonology - S4-E17
Other mistake: Prentiss pulls up to a bar and the shot shows her looking out of the car window. "BAR" is shown reflected in red on the car window, but it is readable from left to right under the closeup of Prentiss's face when we see her. The reflection of "BAR" should have been backwards since it's a reflection of the sign on the building.
Continuity mistake: In the episode before this one, Garcia gets shot and the wound is over her chest. This episode starts when a woman finds her, and the wound is noticeably further down. (00:46:05)
Factual error: The story is happening in Miami, Florida. Many shots show cars and the bad guys' truck with license plates in the front. In Florida cars don't have plates In the front.
True Night - S3-E10
Continuity mistake: When Garcia and Morgan are talking in Garcia's office, her hand on Morgan's chest disappears and reappears. (00:04:55)
Continuity mistake: There's a clock on the first victim's night stand. When she goes to bed, it's Tuesday, 11:06. When the murder happens a couple of hours later, it's still Tuesday, 1:13.
Other mistake: When it shows Keri's license it says it expires in 2003, but the episode takes place way after that year, considering Katrina had already happened.
Continuity mistake: The unidentified subject is cutting a piece of flesh with a fork and a knife. The first shot shows him holding the fork with his left hand. His elbow is up, index finger straight, resting on the back near the head of the fork, the other four fingers wrapped around the handle. Next shot shows him elbow down, holding the fork with all his fingers wrapped around the handle.
Factual error: In the scene where the two unsubs are in the restaurant choosing the next victim, the family they are watching is a Hispanic family that breaks from speaking English for two lines to speak in Spanish. The father asks where the daughter is going, and she answers, "A lavar mis manos," which means to wash my hands. This is incorrect. In Spanish, you would say this as "A lavarme las manos."
Continuity mistake: Before the BAU catches the serial killer Carl Arnold, they used a heat sensor and it shows five people sitting at a table. They said there were three adults and two kids, but when they break in the house, the mother and one kid were sitting at the table, the father was tied up nearby, and Carl Arnold and the other child were in the basement. They were found by Derek Morgan right before Carl Arnold threw the child at Gideon, who fortunately caught him.
Plot hole: In the scene where The Reaper/George Foyet calls Haley from Marshall Kassmeyer's home he identifies himself as Victor Collins from the Marshall Service. Later in the episode Hotch calls Haley and tells her he needs Jack working the case. Jack comes to the phone and asks him "Is George a bad guy?" Until Hotch called Haley she didn't know Foyet was not a US Marshall named Victor Collins.
Suggested correction: He didn't say George.
Character mistake: At the end of the episode, Rossi quotes Anne of Green Gables author Lucy Maud Montgomery, but accidentally calls her "Lucille".
Continuity mistake: When Morgan gets off the phone after talking with Garcia about the list of chemicals he found, the hand holding the phone to his ear changes between shots. (00:13:55)
Magnum Opus - S8-E13
Character mistake: Blake says the unsub must be a universal recipient blood type, AB pos, but they are talking about receiving plasma. The plasma universal recipient is O neg, the opposite of what it is for regular blood transfusions. (00:33:27)
Protection - S10-E22
Continuity mistake: When JJ picks up Lizette Castro in her car to take her to her son, JJ gets Lizette to confess about the man in the pictures. We see JJ stop the car outside In the Dark by some trees before a flashback plays. After the flashback, it looks like the car is in some sort of parking house. (00:14:16 - 00:15:16)