I agree with a lot of things being said here.
I wouldn't show the alien mummy at all. Perhaps just the hand, but make it more mysterious and unkown.
I'd get rid of the whole Doom Town scene. Unnecessary and made the opening a little too long, in my opinion.
Again, I wouldn't show Spalko handling an obvious puppet that is supposed to be the alien. Why they would take this thing to the South American jungle is beyond me.
I'd make more use of the jungle cutter. It is barely shown before it gets blown up. It could have made for a nice fight sequence.
Of course, the Tarzan sequence. Just...no.
I echo what others have said about the waterfall. I think just one would suffice. Also, that would give them a chance to slow it down a bit, maybe develop Marion a little more, her relationship with Oxley, her son, and of course Indy. Maybe showing Mac dropping one of those locator things. At first when Spalko was holding it by the waterfall, I thought it was part of the car. It wasn't until the second time that I realized what it was.
I'm not sure what to do about the skeleton/alien scene. I know I hate that they show the alien. But I don't think the skeletons themselves were scary enough. It needed some work.
Mac's death was stupid. Not that he died, I didn't care about that. It's his response to dying. "I'll be ok," or whatever it is that he said. Is that really something an incredibly greedy person would say right before his death? He had all those things around his neck, perhaps having the magnetic powers of the skull pull him back into the vortex or something would have been a little more interesting. One could make the argument that it's a pretty sexist moment in the films. Elsa, a greedy character, dies because of her greed, and gets no redemption. Mac, another greedy character, gets to realize he is going to die, and then make a clever comment and accept death. I don't believe that was what they were going for, nor do I think they are sexist, but I can see people who study multicultural film making the argument.
Also, how is that Mac had the foresight to hint to Indy that he was a special agent while totally intoxicated and while Indy was in no danger of escaping? This really doesn't make sense, especially given that he wasn't a double agent at all.