While I love the idea of Moriarty as the 3rd brother, I just can't see the logistics. Supposedly mom is the smart one and that's where all three boys would have gotten their brains. So the connection (assuming the 3rd brother would be a bad guy half brother), would be through Mom. Sherlock and Moriarty aren't that far apart in age so how would Mom have hidden the pregnancy? Besides, the parents are so darn cute together, I can't imagine an affair.
However, what if brother #3 was CAM? It explains why Mycroft was protecting him "If you go against Magnussen then you will find yourself going against me" (sounds like a brotherly thing to say) and the almost devastated look on his face as Sherlock replies "I'll let you know if I notice." Also explains why he was so emotional (helicopter scene) when Sherlock shot CAM. Sherlock shot their own half brother and didn't know. Surely Mycroft has ordered the death of plenty of people and though he showed some affection during the Christmas smoking scene, I'm not sure Sherlock killing a nasty would have really bothered him all that much.
Also, CAM seems like he could be older than Mycroft so Dad could have (unknowingly) fathered him in Denmark before marrying their Mom. We don't know what Dad did for a living. (I picture him as a spy seducing CAM's mother, that's why he and Mary get on so well.) And in the books, the third brother was the eldest who managed the family estate (Appledor-ish?).
But why/how would Lady Smallwood and the rest know about a third brother and Sherlock not? Once CAM was dead, Mycroft could have shared the relationship with some of the key people though I don't know why he would--perhaps guilt over Lady Smallwood's husband's suicide in explanation why he didn't stop CAM from blackmailing her? If he had already decided to send Sherlock off to the fatal undercover job, he wouldn't have to worry about Sherlock finding out before he died (in Eastern Europe in 6 months time).
Another reason Mycroft didn't go after CAM could be because CAM knew he was their brother but agreed not to tell Sherlock, Mom or Dad so long as Mycroft didn't interfere with his plans.
All this goes out the window if Sherlock knows about the brother because it can't be either Moriarty or CAM. Despite his "sociopath" personality, I don't think he could bring himself to knowingly kill (or cause the death) of his own brother.
CAM shares the same lack of emotion and human connection as both brothers. But then, so does Moriarty.
It's certainly great fun thinking about all of it.