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.
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)
Magnum Opus - S8-E13
Character mistake: At the end the murderer says Van Gogh only sold two paintings before he died. Van Gogh only had one of his paintings sell before he died.
Character mistake: When Blake is telling Spencer to keep his eyes on her after being shot she calls him Ethan twice. (00:02:29)
Suggested correction: This is very poignant and deliberate moments in the dialogue. Blake is feeling distraught since Reid pushed Blake out of the way and took the bullet instead of her. Blake calls Reid by her dead son's name, "Ethan," when she tries to keep him alert and shouts, "Ethan, Ethan!" Later in the episode, when Blake takes Reid back to his apartment, she explains that watching Reid when he was hurt touched a nerve. Reid then asks Blake, "Who's Ethan?" and Blake tells Reid all about her son "Ethan" who died when he was 9 years old. Blake then tells Reid that "Ethan" would have been a lot like him. Note, on the jet return flight, Blake texted Hotch her resignation from the BAU, and at the very end she leaves her badge with Reid.
Target Rich - S11-E7
Character mistake: When the unsub puts the lock on the woman's collar, he hooks it onto the part where a leash would go. She could easily take the collar off. Later, the lock is on a different hook that is pushed through the collar, so she would not be able to escape. (00:19:10 - 00:33:30)
Character mistake: When Derek and Rossi are in the morgue, you can see the "corpse" swallowing just before the scene changes.
Character mistake: When they are delivering the profile, Rossi says "he's already picked his next victim; an adolescent boy." The victim is a girl.
Suggested correction: Rossi is talking about the next victim after the girl.
Character mistake: Rossi reacts upset to the phone call before the killer starts singing happy birthday. (00:06:25)