I've had general concerns about this as it's definitely happened to me before as well. Things like the soldier using the HEVY Launcher shooting something immediately in front of them, going almost 45 degrees either left or right, or even shooting half as far or twice as far as the target. While I certainly understand the fairly low chance to hit that sometimes comes up, these are supposed to be soldiers pulled from the elite of the elite of the world's military, come to fight against an alien menace. And even though the HEVY launcher is a newly researched item, it's not really that different from many grenade launchers used throughout the world's military. So while there only may be a small chance of hitting the target, it would make much more sense to me if a miss resulted in going a few squares left, right, over, or under. The lower the hit possibility, the more likely to be further away from the aiming point. So some sort of grid or circular template with possible hit chances around the target would make a lot more sense than the current behaviour.
Similarly for throwing a grenade. These aren't civilians who have been conscripted into the fight, and throwing a grenade directly into the tree right in front of them seems extraordinarily unlikely for any highly trained solder. They may not hit the exact square they're aiming for, but they're not going to miss 45 degrees to the right and half the distance they were aiming. Even people who aren't great at throwing objects like balls usually can manage to get it in the general direction they're aiming.
Anyway, that's just my thinking on this, but it would probably entail a significant redesign of the way things work. I totally agree though that the shooting at your feet that happens quite a bit in the game seems pretty ridiculous given who our soldiers are supposed to be.