Continuity mistake: While Morgan and Prentiss are at the crime scene talking to the homeless man, when Morgan moves the tent and finds the text written on the wall, the homeless man smudges the text with his fingers, but when Morgan sends a photo of the evidence the smudges and text differ.
Exit Wounds - S5-E21
Factual error: The BAU is called in to assist the Sheriff's Dept. in Franklin, Alaska (a made-up town, although there is a ghost town by that name). By statute, Alaska has never had any Sheriffs. Functions filled by sheriffs elsewhere fall mostly under the auspices of the Alaska State Troopers. Other law enforcement is by community or (rarely) borough which is what Alaska has instead of counties.
Visible crew/equipment: When JJ and Derek get to the bar to talk to Harris Townsend, while they're still outside in the parking lot, right after Derek tells JJ not to turn her back on the door, the reflection of the moving camera can be seen on the pickup's back window as they walk to the door.
Visible crew/equipment: When the trailer park manager leads Rossi and Reid to Goehring's trailer, right after he tells Reid, "Piece of advice, pipe cleaner, way you're wearin' that gun...beggin' someone to take it off you," the cameraman and camera cast shadows on Reid as he walks by the camera.
Visible crew/equipment: When Hotchner, Callahan, JJ, and Rossi surround Frank's car on the private property, just after Callahan sees the leg on the seat, when she opens the passenger side door the reflection of the standing male cameraman/crew member is visible on the surface of the car, between the windows.
Revealing mistake: When the unsub is in the house with the mother and her toddler, one of the shots of the toddler is flipped, before he starts crying.
Audio problem: When Tabitha gets home, she takes her boots off and as she walks into the kitchen we hear the soft, padded sound of bare feet; when she closes the fridge and walks to the window, her footsteps indicate she has her boots on again.
Continuity mistake: In the scene where the unsub is having a tea party with her "dolls", look at the diabetic woman's right hand when the unsub is pouring her tea. When the tea is being poured the doll's right hand is palm up. When the camera cuts to a close up of the cup the doll's hand is face down. The doll is paralyzed due to the drugs and had not regained control of her body yet, making it impossible for her to move the hand on her own.
Character mistake: In the scene where the agents are called to the conference room and start talking about the case, the camera pans the room and shows a white board with information written on it. At the top of the board, in bold letters and asterisks around it, is the word MANDITORY.
Continuity mistake: During the lake scene, it's sunny when they are showing the suspect and victim driving toward and into the lake, and it is raining when Morgan is shown running after the car and diving into the lake.
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.
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)
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.
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.