The first, which has probably showed up for others, is that most of the time when I'm playing against the computer and the CPU Worm uses the shotgun and after he's taken his two shots the retreat timer doesn't come up and he just sits there until his turn time runs down. If he takes one shot and moves off before taken his second shot, or reaims and misses with the second, the retreat timer comes up and counts down normally.

The second might be a hardware issue. Anyway it usually comes up when I'm using independently targeted weapons, like the Homing Missile or the Air Strike, and I have trouble moving my crosshairs over. It's seems like when I mouse over to the right the cursor seems to hit a brick wall and will start moving over to the left, this also happens left to right as well. I've run into some mouse and keyboard issues on Beat Hazard so I thought might just be an old mouse breaking down rather than a full glitch in this particular, but I figured I'd check it out.

Shotgun thingy with CPU is a known issue sadly...

And the second thing does indeed seem to be a problem on your end.

@2:

Try cleaning the dust from under mouse's bottom (take out the ball if you have one) or use a mouse pad for your mouse. Your mouse doesn't seem to have enough grip.

I'm actually using an optical that's about three years old, and running through a ps2 connection because half my USB ports are out.
Since nobody els has run into I guess I ought to look into a new mouse.
The funny thing is that I haven't had any mouse problems outside of these two games.

I've experienced #2 a little bit I think. Just something I read, try lowering mouse sensitivity settings in Windows and see if it makes a difference.