Disclaimer: While Sherlock Holmes may be public domain, this version belongs to Gatiss, Moffat, and the BBC. I just like to play with the characters.
Mycroft is curious, something that he finds does not happen very often. Things, events, people, and especially people... they are all in this world to be manipulated. They must be investigated simply so he can control them; genuine curiosity has little to do with it. Besides, for the most part, people are predictable. Sex, food, power, salvation, money, fame- Mycroft has had motivations memorized since he was a child. He might need to know the particulars, but he has already recognized what is important.
Mycroft knows the instant his brother decides to look at a flat with Dr. John H. Watson. When he discovers it, he does not automatically rush to pull files on Dr. Watson. Mycroft loves Sherlock in his own big brother way, but he knows more than anyone the full extent of his faults. Sherlock is childish, selfish, possessive, capricious, unfriendly, and many other adjectives that Mycroft really cannot be bothered to put down. And because he knows people and because he knows his brother, Mycroft knows Dr. Watson will not stay long with Sherlock Holmes.
Some light reading on the man might be required, Mycroft muses, if he is one of the few who manages to stay for several weeks. He might even manage a month. However, Mycroft has no doubt that Dr. Watson will simply be one more failed experiment in Sherlock's small folder of attempts to create a socially acceptable relationship.
When Anthea (he believes that's what she has decided on today) comes to tell him that John Watson has followed his brother to a crime scene, Mycroft is slightly surprised. And he is surprised even less often than he is curious, and, in this case, the surprise leads to curiosity. He is genuinely curious about this potential flatmate. Astonishing. He has misinterpreted this Dr. Watson, something that will have to be corrected; he does so hate to be wrong. He makes arrangements to meet the good doctor after he is deserted by his brother, and settles down to read the file on John H. Watson, lately of Afghanistan. By the time he is finished, a smirk once more appears on his face. He thinks he has the measure of Dr. Watson now.
The meeting with the good doctor goes much as Mycroft expected. John H. Watson is a good man, a man willing to die for Queen and Country, a man of principles and morals. He is a man who loves the little things in life, like a warm blanket on a winter's night or a good pint in the local pub. He is a man who is not very emotional, but who understands emotions and who needs that connection with friends, family, and lovers. And yes, John H. Watson is a man who craves danger and the battlefield. Mycroft realizes that because of this, Dr. Watson will probably last longer than any other companion Sherlock has ever had. However, unlike Sherlock, whose need for the Game overrides all other needs, Dr. Watson is not completely ruled by the war. He craves it right now, and will most likely always crave it to some extent, but he will eventually want the small comforts of home, the emotional connection of a spouse. And then, he will leave Sherlock Holmes.
Mycroft leans on his umbrella, just out of sight of the police, and he watches his brother talk to Detective Inspector Lestrade. Mycroft is not particularly surprised that Dr. Watson shot the cabbie; he is a loyal, moral man in addition to being a man of action. He would not let someone die at the hands of a murderer if there were something he could do about it. End result: one dead cabbie.
It is during Sherlock's talk with the DI, that Mycroft becomes more than surprised; he is flabbergasted. He watches in astonishment as Sherlock halts mid deduction and simply stares at Dr. John H. Watson. There is a look in his eyes that Mycroft can only remember seeing when Sherlock was a very small child, and everything was new in the world. It is a look that says What is this strange, wonderful thing? How can it be that five minutes ago I did not know it existed, and yet here it stands before me, as if it has always existed? Sherlock opens his mouth, and, instead of finishing his bout of brilliance, he spouts off some nonsense about being in shock.
And that, Mycroft thinks, is the most astounding thing he has heard in a long while. He knows his brother. He knows Sherlock values his brain above all else, and he knows that the consulting detective loves proving that he is the most brilliant man in the room. He knows Sherlock hates to be underestimated, and any perceived slight to his brainwork is dealt with efficiently and cruelly. And so Mycroft knows how much it must have cost Sherlock to say that he is mentally handicapped in any way, even if it is something as understandable as shock. Yet, for Dr. John H. Watson, Sherlock disparages his own deduction. Perhaps Mycroft does not know his brother as well as he thinks.
Mycroft manages to regain his composure in time to trade barbs with his brother and to unsettle Dr. Watson. He thinks Sherlock does not realize how much he has discomfited his older brother, and that is good. He watches the duo walk away; Sherlock comments on how he can discover a good Chinese place by the door handle, and Dr. Watson unconsciously places a hand on the place where he has his gun hidden.
Mycroft knows he has gotten much wrong today, and he does not like it, but at least he was right about one thing. He watches Sherlock Holmes and John Watson leave the crime scene, giggling like teenagers, and he knows that whatever relationship the two form, it is unlikely to be a socially acceptable one.