The aiming is all off for me on this section of the game. The crosshairs don't match where the lasers fire, and they only fire like half of the time. I have tried changing my mouse settings and vsync on/off but nothing helps. I have watched YouTube playthroughs of this section and they don't seem to have any problem shooting where they are aiming.

I'm fairly sure this is caused by the widescreen patch. If you blow up it lets you just skip this minigame.

Yep, it is caused by the widescreen patch. Best solution is to have a backup of the files the patch replaces, beat the mini-game and put the patch back in.

Since this is the only post I came across addressing this issue, I'll give my solution here.

This is definitely the 'ANOX' widescreen patch. My solution was to extract the patch. Go to 'custom resolution' folder instead of the one you need. Extract it and patch it to 1280x960 (which was the 'Hi-res resolution' in the GCT setup after patching).

You should be able to play the game without the aiming bug. Revert to the original patched files (which you should backup) after the bugged mission and enjoy.

Hope it helps. This is much easier than reinstalling and updating again.