You know what you're right. They should have explained that. You know what else they should have explained? How the heck does Batman have time to apply that black makeup around his eyes every time he gets the suit on? I mean, he changed pretty fast in the penthouse scene.
And when does Batman go to the bathroom? I never saw him go to the bathroom in the movie, so did he not go to the bathroom the whole time?
This is a superhero movie, I mean, come on, we don't need explanations as to how everything happens. The Joker blew up the hospital. We don't need to know exactly how he did it. It doesn't move the plot along or add to the story. There are hundreds of things that happen in this movie that are unrealistic. Batman having a hang-gliding cape for one, falling out of his penthouse, landing on a car, and not breaking multiple bones is another. Joker not being dead when the semi he's in gets flipped on it's head. Two-face not being dead with how severe his head wound was (nobody in real life would live with a burn hat bad).
The Joker rigging the hospital to blow is hardly the most unrealistic thing in the movie, but you know what? The movie isn't realistic! It just uses elements of realism to ground the story so people can relate to it a bit.