One thing that somewhat bothered this troper was knowing that while Indy was having his adventures fighting Nazis, digging up artifacts and rescuing damsels, soldiers were dying in battlefields and civillians were in concentratian camps. Well, perhaps Indy himself was bothered by that too, after a while; we learn in "Kingdom of the Crystal Skull" that Indy joined the army and fought in WWII himself, sometime between the last adventure and this one. Indy was always heroic to this troper, but that just made him even more so.
Slight problem with that theory, as the first three IJ movies took place from 1935-1938, and WW 2 didn't begin until 1939. So while Indy was off combating Nazis and foiling their plots, none of Britain, the U.S.A., France, Russia, etc were even engaged in war yet. So yes he was a hero for joining the army in WW 2, but he was even more of a hero before that when he alone of his countrymen (or even the free world) was fighting Nazis.
Remember in 1936, the year Raiders was set the summer Olympics was actually in Berlin with Hitler presiding over the ceremonies!
Keep in mind that most people didn't know about the concentration camps until the war was almost over anyway, and even then most reports weren't believed. Americans joined in late 1941 and only after being attacked, it had nothing to do with Jews or concentration camps or their allies being killed.
Also remember that Indy fought in WWI as an American volunteer in the Belgian army. Not only did the horrors of war scar him and ruin any "romantic" notion of fighting and killing, he also came to realize that it was not his job to right the wrongs of the world all by himself, which is why he didn't get involved in WWII beyond what his job and personal obligations dictated until the U.S. formally joined the war.
Indy is noticeably more muscular and buffer◊ in Indiana Jones and the Temple of Doom than he is in Raiders of the Lost Ark even though it's supposed to be set a year before that movie. The reason behind this is because Indy would be shirtless through a lot of the movie so they had Harrison Ford work out with a personal trainer to build up his body. If you look at the one shirtless scene in Raiders (when he's on the ship with Marion) he looks scrawny in comparison◊. In Indiana Jones and the Kingdom of the Crystal Skull Indy mentions to Mutt that he almost died of typhus looking for the lost city of Akator. Typhus can cause dramatic weight loss. It's possible that between TOD and Raiders is when Indy got typhus and lost a lot of muscle mass and that's why he's skinnier in Raiders.
Also notice that Indy is refering to a novel that was published only in Germany which has him searching for the city, then known as El Dorado.
Indy never finished high school (leaving halfway through his senior year to go fight in WWI) and yet has no trouble getting into college.
His father was a renowned historian and he learned several languages and advanced history from an early age; the real question is why he would even need to go to college in the first place, except to get the credentials so that he doesn't have to show off every time someone asks him to prove that he's qualified to be an archaeologist.
If he wanted any sort of actual, professional career, the credentials would have been a requirement. As to how, um, GED?
Not to mention, Indy wasn't exactly a "dropout", but a good student that left to fight in World War One (okay, not through the usual route, but he did). I can't say for sure but I would imagine that soldiers had facilities to reinsert in civilian life.