I've been through some of the previous FAQ answers that touched on this battle and they were very helpful, but I didn't see anything addressing this point. The scene repeatedly shows cannon (horizontal, not mortars) firing, and then explosions happening where the shot lands. I had the impression that field artillery of this era was still pretty much just firing roundshot, but maybe roundshot isn't cinematic enough unless it hits a guy right in the head?
What you see in that clip is a very common film effect, the "mortar". It's basically a pot full of fine dirt sent flying with compressed air. It's cheap and easy and fairly safe to have around people, yet makes a big showy "explosion", and is quite popular therefore. You can add a bit of fire to it with some propane or gasoline, which I see a few times, but mostly it's just dirt flying.
My understanding is that field guns of the time would only use solid shot, so if we want to be charitable to the film makers, you can read these as the impact of cannon shot with the ground; later in the scene they CGI a bouncing cannonball with some of these "mortar" effects, which suggests they knew what they were portraying.
What we actually see doesn't really make sense with the occasional fireball, is probably exaggerated in the amount of dirt that would be kicked up, and the trajectory of the dirt isn't plausible. But that's movie making. And it's also not the least accurate thing about The Patriot.