Disorder(s): Schizoid personality disorder, obsessive compulsive personality disorder [bureaucratic compulsive; not to be confused with obsessive compulsive disorder (OCD)]
Positive traits: Extremely high intelligence, ability to identify weaknesses and attributes in others, strong ability to understand and predict the actions of others (and identify the motives for those actions), highly observant and perceptive to detail, extremely self-aware, strong sense of duty, high level of patience
Negative traits: Inability to empathize with others, constant need to intimidate others, constant need to repress emotions, tendency to be controlling to the point of oppression, tendency to set unattainable high standards for self or others
Notes: Mycroft has certain notable similarities that he shares with Sherlock Holmes, such as his high intelligence and cold personality, which is unsurprising considering two things: 1) they are related, and 2) it appears that Mycroft may have been the one to teach Sherlock how to be cold and emotionless in the first place.
He is, however, notably different as he is much more careful than Sherlock; unlike his brother, he takes responsibility for his actions and is cautious when it comes to causing or diffusing trouble. He is also more selfless, as he has a strong sense of duty (devoted to his country and the British government).
These differences between Mycroft and Sherlock may culminate from the fact that whereas Sherlock had most likely never had to take care of a human being before, Mycroft probably spent his childhood or at least a significant part of his childhood being Sherlock’s primary parent figure. There is strong evidence that suggests that the Holmes family was a dysfunctional one, and Sherlock’s parents may have been largely absent or lack the facilities to give proper support and care; this explains Mycroft’s rather motherly nature, as he seemed to be the surrogate.
Mycroft, however, is also very controlling, nearly to the point of oppression. He engages in power play to show dominance (kidnapping John Watson instead of simply calling him, which leads John to very astutely point out Mycroft’s “bloody stupid power complex”), and this may be one of the reasons that Sherlock dislikes him so much (Sherlock particularly dislikes being controlled or having his freedom limited). Mycroft may also have a habit of underestimating people or being too confident. He is very used to being in charge, and thus he may accidentally do something reckless under the facade that he really has everything in control. This may have been the reason he inadvertently spilled information about Sherlock to Jim Moriarty. However, afterwards not only did he feel guilty about it (which is very notable since it most likely takes a lot to make the Iceman feel guilty; he must really care about his brother a lot), he did his best to try and warn John and remedy the situation, which shows his responsibility. However he did not admit his mistake until much later, which shows his shame and also his large but fragile ego.
Mycroft is also clearly antisocial, albeit not as prominently as Sherlock (he at least makes an effort to seem polite or affable, which Sherlock does not, unless he is attempting to manipulate someone); he spends his time at the Diogenes Club, a club made for men who “enjoy soft couches and tea but dislike communication”.
Mycroft is also very rigid and strict; he is what most people would say “prim and proper”, except to the point of OCPD.