Boo Radley is a Heroic Albino.When Scout finally meets him in person, he is described as being ghost-like, with very pale hair and skin. Scout, not knowing what albino is, would just assume this is because he stays inside all the time, rather than Radley being born like that. This would also explain why Radley is familiar with the doctor; he probably would have medical problems which often come with albinism like bad eyesight. It might also be partly why he lives such a reclusive life, as if he was an albino he would be easily identifible in a small town and rumours could spread easily about him, (especially in 1930's Alabama).
Bob's kids have different mothers.Although Bob Ewell sexually abused Mayella, the story has never mentioned her being pregnant. So maybe she isn't the mother of the kids. Bob maybe had kids with various prostitutes.
Boo Radley is a War VeteranOne of the gifts that Jem and Scout find left behind by Boo happens to be a war medal. Assuming Boo Radley is in his late 20s or early 30s he would have been old enough to have fought in World War I. If he is a war veteran it would explain why his behavior is so odd, he is suffering from Shell Shock or what we now call Post-Traumatic Stress Disorder. Boo Radley giving up a war medal to these children shows how much he cares about them, he's reaching out to them with a symbol of the experiences that caused his trauma in the first place.
Decades before the book takes place, Atticus Finch murdered a black man.Atticus Finch, the man of morals, hates injustice. He especially hates when a white man abuses a black man. "There's nothing more sickening to me than a low-grade white man who'll take advantage of a Negro's ignorance." As a youth, he was an exceptional marksman ("Ol' One Shot") but for some reason he gave up shooting ("haven't shot a gun in thirty years"). According to Scout, he "hated guns and had never been to any wars" - which, if true, would seem to rule out the possibility of his aversion to guns being due to experience in war. Miss Maudie DOES say "I think maybe he put his gun down when he realized that God had given him an unfair advantage over most living things". However, perhaps as a youth, Atticus was racist - perhaps even a member of the Ku Klux Klan - and actually either directly murderered a black person himself or participated in a group murder (lynching). That could go a long way toward explaining both his especial hatred of white abuse of blacks and his strongly held belief that he was morally obligated to defend Tom Robinson and that he couldn't face his children if he didn't.
Boo Radley has social anxietyThe intense shyness and fear of going out in public seems cute and endearing when Beth March or Laura Wingfield has it, not so cute when it comes from a young man in a small town.
Boo Radley is gayAnd Miss Maudie saw fit not to mention it to young Scout. Him and the gang of young friends he was caught with might have been caught "experimenting," or in a part of town known for queer activities, or one of the kids may have just had a reputation. Anyway, it was the accusation (or even the suspicion) of homosexuality which drove the elder Mr. Radley to such an excessive abuse towards his son.