I am confused. I've played SWAT 3 before, and I don't remember this. But now it seems I can't shoot while moving? I have to have been standing still for an entire second before I can shoot? Is this normal?
I'm using the Last Resort launcher, but with the mod turned off.

There's nothing like that in my game but I don't use any mods, just the vanilla game with the dgVoodo wrapper and an ini tweak to have the resolution I want and good performance.

Mods won't have any affect on that sort of thing. The only thing mod makers can do really is speed up or slow down player movement. The mod would also have to be designed specifically to affect the "swt_data.dat" file.

As for the Last Resort mod it doesn't affect movement at all and besides when you have it toggled OFF you are playing vanilla Swat 3.