a selection from the TV Tropes entries for Mycroft [link]
Memetic Badass: Both Mycroft and his umbrella
Fatal Flaw: For someone who claims he’s not big on sentiment and doesn’t think he has basic human decency, almost every major mistake Mycroft makes onscreen is because he loves his sibling. Correction, siblings.
Beware the Quiet Ones: He may seem like a sedentary government agent type, but if you threaten his family or his country, he’ll pull some strings to fuck you up. In making decisions, he appears even colder than Sherlock.
Good Is Not Nice: Devoted to queen, country, and little brother, but definitely not one of the angels.
Love Is a Weakness: Firmly believes that “caring is not an advantage”, which in a nice case of Dramatic Irony is used against him because Moriarty, Irene, and Magnussen all know that the best way to get to Mycroft is through his little brother.
Lonely at the Top: He is seen sitting alone doing nothing on Christmas Eve in “A Scandal in Belgravia”. Of course to him it may be a special luxury to do so. In fact he seems to prefer being alone.
Mycroft, who not only is the British government, but can fake plane crashes and order assassinations.
Sharp-Dressed Man: Always seen wearing fancy suits.