Mario creator Shigeru Miyamoto cleared up a series of misnomers about the portly plumber's lore in an illuminating interview at GameInformer.
Miyamoto explained that Bowser children, the Koopalings, are actually adopted. "Our current story is that the seven Koopalings are not Bowser's children. Bowser's only child is Bowser Jr., and we do not know who the mother is," he said. This does nothing to explain where he got all those kids from. I guess the Mushroom kingdom has lax adoption policies.
When asked why Mario and the gang play tennis and go-karts with a known kidnapper/thief/murderer, he cited Popeye as an inspiration where characters take on different roles while still maintaining a few distinct personality traits.
"If you're familiar with things like Popeye and some of the old comic characters, you would oftentimes see this cast of characters that takes on different roles depending on the comic or cartoon. They might be businessman in one [cartoon] or a pirate in another... It's more like they're one big family, or maybe a troupe of actors."
Elsewhere Miyamoto explained the origins of Mario's mismatched facial hair and 'do. Initially it began with the limited colour palettes at the time.
"Mario was originally red, blue, white, and black. Maybe it was around the time of Super Mario Bros. 3 that we changed his hair to a different color. What really happened was that, when drawing the character, it became much easier to draw the mustache as an extension of the outline of his nose. Using that same color of black, we drew the mustache. But then we felt bad for Mario that he didn't have a distinct hair colour, so we gave him brown hair."
Finally, when asked about Mario's various professions as a plumber, carpenter, athlete and doctor, Miyamoto noted that doctor didn't belong and the general rule was to give him blue-collar worker jobs.
"There's really only one rule in terms of the things that Mario does. Generally, it's that he's more on the blue-collar side. He's hard-working, and certainly much more physical in nature. So, I think that a doctor is sort of an unexpected and perhaps unbelievable role for Mario. Perhaps the Dr. Mario you're thinking of was maybe, in some way, not necessarily legitimate."
We're going to take that to mean that Dr. Mario is an illegitimate quack. Patients beware!