I would for sure add the new Lucasfilm logo from crystal skull, and of course change the title to "Indiana Jones and the".. I really like the idea of making the titles more like crystal skull and crusade. I would also like to add in the new digital shot of the truck going off the cliff that showed up on an HD broadcast if I'm not mistaken, if someone has a good capture of it that is.
I would probably remove Marrion's line "oho, oh nooo" when the mokey knocks over the juice or whatever when they're with Sallah's family. I think it sounds really dubbed, and odd for her (if it is indeed supposed to be her). In terms of audio, there's a couple other small things I'd change, like the lines/mutterings coming from the guys that fight indy in marrion's bar. They sound very dubbed and "odd" in a few places. I would also love to add in some new punching sounds like in crystal skull (if they were indeed new... is it just me or did those punches sound extra intense).
I have also never understood how jock (the guy who flies Indy away in the beginning) could possibly see Indy running from all the natives when he looks up and it cuts to Indy in the field. If some sort of visual effects trickery could be used to alter the shot of Indy in the field to show how he may be visible, I would be very much in favor of that.
I'm super tired right now and can't really remember anything else that has always bothered me, but I will post more when/if i remember it (or if I can come up with anything else lol, raiders is pretty damn good). I would still love seeing these things changed and totally merits an edit IMO. I'll probably end up doing this stuff myself one day if no one else does.