Originally Posted by BatLobsterRises
Then you're getting more into the plot mechanics in a discussion about characterization.
I can't really think of a good reason to justify how and when The Joker wired an entire hospital to explode, but ultimately I don't care because seeing The Joker walking out of a hospital in a nurse uniform as it blows up behind him is one of the most Jokery-things imaginable. The movie took a shortcut, but it's fun and terrifying to see what The Joker is able to accomplish without being given every little detail about how he worked it all out. It helps with his unpredictability factor, which is important to the character.
Also things like the firetruck on fire, the "clapping" scene, (s)laughter is the best medicine etc. really showed perfectly Joker's dark sense of humor and taste for the theatrics.