I have to say I didn't find very much in the films to be 'disturbing'. The treatment of the character of Faramir I thought was just wrong, and I didn't even register that Gimli might have been sitting on a slaughtered Orc, possibly as I'd just been watching a huge battle scene and my senses were filled with the noise and smell of war (or something like that

).
However, one scene I found quite scary in a stunning way and that was where the beam of light shoots up from Minas Morgul and the sound on the film cuts out for a split second - that was incredibly effective as a 'horror' moment for me.
Now there are in fact a few scenes that I do not like watching as they make me feel a bit uncomfortable - any scenes where animals seem to be hurt or slaughtered. I don't like watching the Oliphaunts stampede the Rohirrim horses, nor do I like it when the Fell beast swoops down and takes horses in its mouth and flings them aside. I find myself looking away at those moments as I find it unpleasant and unsettling.
But I wouldn't say there were
disturbing scenes - as I always manage to comfort myself with the knowledge that this is all just smoke and mirrors, they are computer generated horses, not real ones. And yes, I also feel sad when the Oliphaunts get stuck full of arrows. Poor creatures.