I'd remove the falling through the world.
And map shooting to left mouse down instead of up or click. It feels very weird and throws the timing of shooting off to have to have the mouse come up before the bullet is fired.
A little antialiasing wouldn't hurt either. Cram 4 pixels into every one and you'll be looking good.
oh and WASD being forward/backward/strafe and mouse for movement and aiming would make this feel right