Batman is a particularly entertaining superhero because he is in some sense the most realistic. There's no need for an alternate universe or an elaborately fictional back story: he's a guy with a cause and enough money to acquire the tools he needs. This premise was violated by certain plot elements in The Dark Knight Rises (see here), but the basic believability of Batman remained.
It turns out that Scientific American has not one but two posts on the science of Batman. The first piece, from 2008, answers such questions as, "How long would Bruce Wayne have to train to become Batman?" and "How would Batman get enough rest?"
In the more recent post, Paul Zehr tackles questions like "Why are Joker and Bane so difficult to beat anyway?" and "What revisions to the Batsuit are needed to protect against... concussion and spinal cord injury?" If these thoughts keep you up at night, you might also be interested in Paul's book, Becoming Batman.