Yeah, Marion's 'Trust me!' never irked me too much either - it explains that her driving off the cliff wasn't just some weird spontaneous move, but a thought-out manouvre (there's a shot earlier where we see Marion peer over the cliff from the jeep). Also, it was a nice role-reversal as well; usually, Indy's the brash one, telling people to just trust him as he blunders through, but here it's switched.

About cuttng Indy being fired and then made vice dean at the end, it would be hard to cut Indy being fired (with this being how he is wanting to leave the country on the train, and how he runs into Mutt, and takes up the quest for the Skull), but perhaps cutting Indy being made vice-dean at the end could be done more easily - there's only one brief shot of Charlie walking past the door with the lettering being put on it, explaining that Indy's been promoted, so this could be cut quite easily I'd imagine. I guess it doesn't really make sense for Indy to be promoted; it's never explained exactly how this promomtion came about, what with the Crystal Skull adventure having no bearing on the university whatsoever.