I've seen a few other threads about this:

After defeating the KPA tanks, the hostage and that OTHER GUY disappear.

BUT: my objectives didn't get updated.

I found where to go (head inland, and find a second waterfall)

and there were a load of rather nice gentlemen that I had a minor altercation with, buuuuuut:

my objectives have still not been updated.
Should I just keep going? Or should I head back to the hostage village and trigger something I missed?

Oh yeah:- patch 1.2 already installed

I've played Crysis a couple of times and encountered this bug once. I went up the waterfall and into the next level through the caves, but I knew where to go. Unfortunately I can't remember if/when the objectives display came back.

I ''think'' you have to exit the game then come back and reload the level.

I just kept going until I found the cave at the THIRD waterfall.
Then everything when back to NORMAL

Odd thing, it said something like 'find cave - objective complete' even though I'd never had any such objective.

I encountered this second time through with patch 1.1 and could find no way of triggering the objective update. For me, the hostage and other nano dude wouldn't leave that room, despite all tanks being blown. Like others have said, I knew to head up the waterfall so once convinced I would not be able to trigger the objective, I finally just headed up and found my way to the cave. Surprised this still isn't fixed in patch 1.2.

Boss had the same problem, in that area and other areas, told him never to use quick save/loads and he never had it again.

yeah there's supposed to be a problem with the quicksave feature that still hasn't been fixed despite the release of two patches. You may want to replay the level on easy without using quicksave at all (though it's ok if you save manually through the menus).