Throughout the movie, the Joker shows remarkable comfort with military-grade weaponry like grenades, explosives, and machine guns, and after extensive Googling followed by a visit from two very nice federal agents, I can tell you that you can't learn how to use that stuff from the Internet. I'm also pretty sure that you wouldn't be able to blow up whole building complexes or hit a moving vehicle with a rocket launcher from inside a speeding truck without at least some practice. And unless the Joker grew up in the city from the GTA games, the only place he could have practiced that is the military.
That's not even my own stupid opinion. That's actually one of the "official" possible origins for the Joker found in The Dark Knight Manual, a 2012 tie-in book for The Dark Knight Rises.
"You want to know how I got these scars? Only $28.65! Order now!"
Actually, a stint in the military would explain a lot of other things about the character, like the, well, military precision of his tactics, including the time he killed a guy using a precisely timed school bus. Plus, there's this seemingly random piece of dialogue the Joker says in the movie:
"I tell the press that, like, a gang banger will get shot, or a truckload of soldiers will be blown up, nobody panics, because it's all 'part of the plan.'"
Of all the things he could have used as an example, it's interesting that the Joker would bring up soldiers getting blown up, especially as shrapnel wounds would be the perfect explanation for his scars. Add some inevitable PTSD into the mix and suddenly you see Ledger's Clown Prince of Crime for who he really is: an ex-soldier who became disfigured, snapped, and later spent the entire movie killing mayors, district attorneys, and police commissioners, aka people who in his troubled mind were representatives of the government that sent him to war.
The clothing choices of a man who's sick of camo.