No matter where I click, trying to cross the abyss, Indy falls down to his doom.
I went as far as looking it up in the walkthrough ( http://indyguide.mixnmojo.com/lcindex.shtml ), because of getting fed up with it (the Grail Diary PDF that came with the game doesn't have any hint for that trial, it seems to be cut short), but clicking the spot it marked doesn't work, either.

At least ScummVM version allows to save anywhere (despite the warning in front of the Temple, that you won't be able to save past it), because having to do first two trials over and over was driving me up the wall after a couple of times.

I managed to do it.

For anyone else having a problem with it: it seems you have to click the right spot on the other side without moving Indy about at all first, otherwise he falls down, when trying to cross.
(if you need help picking the right spot, the walkthough I linked in my previous post shows it)

Yes, you must have faith and do not hesitate...
Btw. I don't think you need to click exactly there, I remember just clicking on the exit and it worked.
I also remember feeling quite stupid after being stuck and this puzzle for a while...

Not how it worked in the movie, I just watched the scene ( https://www.youtube.com/watch?v=xFntFdEGgws ), and Indy hesitated a good bit. So I feel sort of excused (but then, they intentionally didn't copy the movie scene-by-scene, or there'd be no puzzles for anyone who saw it).

The trials as portrayed in the movie (and at least first two in the game) seem to be "just" feats of engineering, there doesn't seem to be anything supernatural about them (blade at just the right height so that you will survive if you kneel* - well, not sure how that applies to the other blades, maybe you could just wait for them to pass and then move on? Second one just had all the "wrong" tiles being too weak to support the human's weight, and third one seems to be just an optical illusion, especially seeing as it became permanently visible, once Indy tossed the sand or some much on it after crossing).

Don't ask me to explain the Grail (and the seal not letting it be taken outside) using science, though. ;)
(I could come up with some wild hypothesis involving aliens and/or Atlantis, but no clear explanation, using only the scientific knowledge actually available to us ;)

*but what if you were really tall?

As for the second part of your post (about just clicking on the exit), I recall doing just that and falling down, but maybe I moved about first (I uninstalled the game already, so can't check it again).

Speaking of science: The 3rd trial looked nice in the movie but the optical illusion only works if you look at the bridge from one specific location. Just moving your head a bit to the side/up/down and it wouldn't fool your brain anymore...

Back to the game: Overall the 2nd trial worked great for an adventure type of game but the others didn't really that well.
Otherwise it was really neat to have the game follow the movie quite closely (btw. I've played the game before I've seen the movie).

I am not sure, but I believe it is possible to get irreversibly stuck if you use SCUMMVM to save during the third trial, as the solution is to click to the other side of the chasm without moving or hesitating, so if you save your game during the third trial with SCUMMVM after you moved around a bit, or after Marcus tells you to go faster (something that is impossible to do if you play the game through Dosbox) you will get stuck in an unwinnable situation, unless you restore a previous savegame.

5 years on... Yea when Indy turns to tell Marcus he's hurrying, it does seem to throw off and fall into the abyss...

When you do, you just end up back at first trial and this time i just pushed through and walked across first time. Annoying but there we are.

Wish I could just beat the stones puzzle in the final room on FOA.