Does anyone else find that they spend a good portion of their non-town time running around while looking at the ground, trying to make sure you get the loot from all of the enemies you just killed? Or, you see some interface message pop up quickly and disappear, so you turn around and try to figure out what made that happen?

Try pressing z, it highlights any stuff you can pick up or interact with.

Yeah the looting needs some work. Sometimes it feels like the 'hitbox' for looting is really small, and you have to position yourself very carefully to pick up certain items.

I think that's because whether you can loot is dependent both upon where your character is and the direction your camera is facing. Sometimes you don't have to move your character at all, but you have to swing the camera around (which is basically why I always feel like I'm looking at the ground).

Pressing shift to walk up to a lootable item helps heaps so you don't keep overshooting the looting zone.