So what is the deal with religion in the Indiana Jones universe? Raiders seems to prove the Abrahamic God exists, Temple of Doom seems to prove Kali exists, Last Crusade seems to prove Christianity, Crystal Skull seems to prove that there are aliens with supernatural power. How can this all be true? Which religion is correct in-universe?
Since Christianity is descended from Judaism, Christians accept that the the God of Christianity is the God of Judaism, so there is no conflict at all between Raiders and Last Crusade.
As far as Temple of Doom proving that Kali exists, this is not an issue either. It is clear in the context of the film that Kali wields supernatural power and demands human sacrifice, so Kali would be just a powerful demon and nothing more. This fits well within the beliefs of both Judaism and Christianity, as you can find examples of such demons in both the Old and New testaments of the Bible.
As far as Crystal Skull goes, no problem there either. Alien life is no problem for most Christians; Pope John Paul II said in 1996, "truth cannot contradict truth. If aliens do exist, then Catholics should have no problem accepting it. We do not have to fear their creation as God is behind it." As for them demonstrating supernatural power, how do we know it was supernatural? Arthur C. Clarke famously said "Any sufficiently advanced technology is indistinguishable from magic." So maybe the magic we saw in Crystal Skull was nothing but very advanced technology.
So, in answer to your question, it would seem that in the Indiana Jones universe Judeo-Christianity is the correct religion.
Where would Shiva fit in? He presumably exists since his artifacts (the stones) really glow.) Maybe Shiva is just another "face" of the Judeo-Christian God?
Okay, so where is Indy's college exactly? Last Crusade and Crystal Skull both show his plane leaving from New York, but Raiders shows him leaving from San Francisco. Surely he didn't travel across the whole country just to get a flight.
He got a new job in between Raiders and Last Crusade?
No, that can't be. Last Crusade clearly shows him teaching in the same classroom he used in Raiders. Plus, Brody was still there and Crystal Skull copies an establishing shot from Raiders (except with '50s cars instead of '30s cars).
In "Raiders" he was going to Nepal. He'd likely have taken a train or plane cross-country to reach San Francisco. Back in the '30s the only way to cross the Pacific fast was on Pan American Airlines' flying boats (service had just started a year or two before the movie). It's more likely that the classic "Indy travelling the globe via red line" montage skipped a step of land travel, I think. Whereas to cross the Atlantic he would leave from a major port like New York- and by the '50s, international airline service was good enough he could easily catch a flight out of New York. The thing to remember is that in this era there wasn't an international airport for every city of respectable size. People trying to fly out of the country had a relatively short list of options.
The plane you are referring to is the China Clipper, which started service in 1934 (although as the last of those crashed in 1945, the plane featured is a Short Solent 3 — owned by Howard Hughes — which first flew in 1946).
He DID get a new job between Raiders and Last Crusade — sort of. In Raiders (and presumably Temple of Doom) he taught at Marshall College in Bedford, Connecticut (filmed at Yale University in New Haven, Connecticut). In Last Crusade, he taught an archaeology class at Barnett College in New York City, but remained a tenured professor at Marshall, where he was seen working in Crystal Skull. So it was the same classroom in Raiders and Last Crusade; he was teaching at the same college. Bedford, like its real-life counterpart, is close to New York City, which had the nearest international airport.
In the video game, when he travels to Venice, we first see him riding from San Francisco to New York...
No it doesn't...also, in his office, he refers to something sent to him by "some people from San Francisco."
Why does he use a whip? OK Rule of Cool, and the plot contrives it so having a whip frequently comes in handy, but is their ever any concrete reason given why Indy favours a whip as a weapon? I know the intro to Last Crusade gives a pseudo origin story for the whip, but even then, how does "once used a handy whip to fend of a lion" translate into a whip becoming his Iconic Item?
The whip was George Lucas' idea, inspired by Zorro. In-universe, it's a pretty versatile piece of equipment. It can be a rope, a harrying weapon, and there is at least one report of a bullwhip being used as a hunting weapon.
Also it scares the shit out of people, which is always good when you constantly rely on the Indy Ploy.
Didn't the guy that apparently inspired Indy's choice of hat in the entire introductory segment of Last Crusade have a whip also?
No, he didn't. Indy got the whip out of the lion tamer's car.
Which is another good reason to carry one in the jungle, as it can also scare the shit out of animals.
The Raiders novel has Indy recalling how he developed his fascination for the bullwhip, seeing a whip-act in a travelling circus when he was seven years old. Obviously, the origin story in Crusade came later.
At least one source indicates that fellow whip-user Catwoman does it because few people know how to use a whip effectively, so there's less chance of an enemy turning it against her. Maybe Indy follows the same logic?
Indiana being a highly successful and respected archaeologist seems like more of an informed attribute than anything, at least going by his success rate on the movies. In Raiders, he lost the golden idol to Belloq, and while he does return with he Ark, that was never made public. In Temple, he fails to return with the Sankara stones. In Last Crusade, he gets his only real hit by returning the golden cross of Coronado, but by the end of the movie the Grail and everything involved to it was lost. And finally, in Crystal Skull, he once again fails to return with the titular Macguffin.
To be fair, there's probably oodles of successful digs and priceless historical finds and reputation-making discoveries to Indy's credit that we don't see, but since they no doubt offer less opportunity for punching Nazis and running away from supernatural beings, there's also a reason why we don't see any of them. Plus, with regards to the very first example, it's less that he 'lost' the golden idol and more that Belloq shamelessly stole it from him.
Indiana Jones is kind of a respected archaeologist. We get a flat-out statement in Temple of Doom that Indiana Jones has a reputation and it's not all that good. Given he engages in what would blatantly be considered black-marketeering, grave-robbery, and outright theft today, it's no wonder. Remember, Indiana Jones started as an Antihero in Raiders. He's also fairly decent at getting small jobs done (as we see with, "They're good pieces, Marcus") but the big history-making scores elude him. Honestly, Indy's Greed is his tragic flaw as finding the ashes of a Chinese Emperor would be enough for most people but he wanted the Peacock's Eye more.
Also, Indiana Jones did return the Sankara stones, or at least one of them. Whereas mercenary Indiana could have given them to the Indian government (or, more likely, somewhere more likely to make him famous), he chose to give it back to the village it came from. Honestly, that was actually the most appropriate display of archaeological ethics he's done so far.
Indy's dad lampshaded this really well with his "you call this archeology?" remark.
A big problem from a narrative perspective are that the discoveries Indy makes in those movies are simply too big. Like yeah, they can have him returning with the Cross of Coronado because ultimately it's just a cool relic. On the other hand, the Ark, the Grail and the Sankara stones are proof that the supernatural is real, with the first two being proof that the Abrahamic God is real AND the stones indicating that He is not the only God out there. On top of that you have the brouhaha with the crystal skulls which is proof that there are beings from another dimension and they have visited earth. Each one of those would profoundly change society as we know it, and his career would be basically over because all the fortune and glory would go to Indy.
What's the purpose of Indy's glasses? We see him wearing them while teaching in college or at the dinner scene in Temple of Doom and he puts them on to translate the Latin text in Donovan's house at the beginning of the Last Crusade. Yet he doesn't seem to need them to read while doing field work during the whole series and he seems to be able to calculate distances. Plus he's not a particularly bad shooter without them, so we can infer he's got no sight problems. We know he's not hiding behind them since everyone knows he's an archaeologist and the Nazis could never connect him to their loss of the Ark. We can see that Jones' girl students fawn over him anyways so we may rule out that he uses glasses to shield himself from girl-lust. Also, he didn't need to use them at all in the dinner scene in Temple, but he did anyways. Moreover, he doesn't wear glasses when he's a lot older during the whole Crystal Skull film. So, why would he use the glasses?
Maybe they are just his Brainy Specs to make him seem more distinguished, respectable and Professor-like? A bit of staid respectability seldom hurts an academic career.
They could just be reading glasses that he doesn't strictly need, but makes reading easier for him. Remember that he did take a blast of steam right in the eye during WWI, so that may be catching up with him. In Crystal Skull he does misjudge the distance of his swing.
If he's farsighted, not having his glasses wouldn't impede his ability to judge distances. Most of the writing we see him read in the field is in the form of inscriptions on walls or artefacts, which probably use a larger font and/or can be seen from a sufficient distance that he doesn't need his glasses; it's the much smaller print in modern books that his spectacles help with.
He's also seen using them when Henry is explaining and pointing to the clues in his diary, so they're likely for reading.
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?
It's the 1920s and 30s. Many jobs held looser requirements compared to what we have today.
Also Indy was no slouch as a student, he could easily have done enough extra credit assignments to earn enough credits to legally graduate even if he didn't finish the year.
Not to mention, Indy wasn't exactly a "dropout", but a good student who left to fight in World War I (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.
You are forgetting that these movies take place in the 1920s and 30s. Things were much different back then - it wasn't uncommon for people in Indy's generation to hold jobs that nowadays require a master's degree or higher. As for how he got in, remember that the most common way to get into college was to have connections. What do you know, his father's a renowned historian and that's a good way to get your foot in the door.