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)
God Complex - S8-E4
Character mistake: Spencer says that leg transplants are medically impossible, however, there was at least one documented successful double transplant performed a year before the season aired.
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.
