Are you sure you want to show WAR movies to your 12-yr old son? If you want to teach him the brutality of war, I'd understand, but most war movies these days are too twisted for kids, IMHO... I wouldn't worry too much about the violence (they get more from video games), but the portrayal of people mentally challenged in a war is something a 12-yr old might not be able to fully digest.
Okay, enough of parental discretion... I hope you are not offended...
Back to war movie recommendation... I would say Thin Red Line is one of the best war movies I've ever seen that actually shows a WAR. No hidden agenda, no lecturing, no simple good vs. evil setup... The movie just shows a war the way it is, especially the people in it, IMHO.
Speaking of war movies with twisted people in them, I would put Apocalypse Now on the top of the list. I try to watch it about once a year, and every time it shows me something different because I'm not the same person who watched it the previous year. I feel there is still so much more about the people in that movie, which I have not comprehended yet... I guess Jarhead had similar intention, but didn't even come close to Apocalypse Now.
One great movie I wouldn't mind my 12-yr old son (mine is a lot older, but if I had one that young) to watch is an old B/W movie titled Stalag 17. Well, it's not exactly a war movie because it is staged at a POW camp. But, it is one of the greatest war movies on my list. And for some reason, I still hum "When Johnny comes marching home again" all the time. I just can't help...
If you are more interested in what goes on behind the battlefield, I would recommend Tora Tora Tora. It shows an honest picture of what goes through the minds of the decision makers on both sides (the US and Japan during WWII) who put their own young men's lives on the line. Tora Tora Tora is a joint production between a US studio and a Japanese one, so it is not as biased as most other WWII movies.
You mentioned Black Hawk Down, and if you have not done it yet, I would strongly suggest watching the documentaries that are included in the 3-disk deluxe set. Especially the History Channel documentary will mean a lot more if you watch it after the movie. You see the real faces of the soldiers appeared in the movie, and it really hits you that Black Hawk Down was not just a movie. It snaps you right back to reality and gives you goosebumps.