So, I've read that using mismatched RAM can cause problems. True? And if so, what kind of glitches?
My brother gifted me his old computer which only had 1 gig of memory (2 500 MB sticks), so I pulled the 2 1 GB sticks out of my dead computer and installed them. Seems to be okay.

It may, due to timing issues.  Most avoid just because it's an avoidable thing to buy matched pairs.  That's great if it works.
 
The memory will probably all run at the speed of the slowest module, even if some are faster in spec.
 
And it may default to single channel memory, rather than dual channel memory, if the channel pairs are not matched modules.  Ultimately it is up to the BIOS how compatible things will be.  YMMV.

What abacab says.  I work the Dell forums and we see many problems from users "mismatching" memory or memory brands.
 
I had this on my own desktop.  I have some Corsair and some GSkill.  They are both the same speed memory, listed as compatible for this motherboard by ASUS.  The Corsair OR GSkill will work in my ASUS Z170 desktop, but not both.  If I install both it will not boot and gives a "POST" memory error.

Mismatched RAM can cause *major* instability.
RAM isn't that expensive.  Use identical sticks... and never worry about it.

RAM errors can also cause some of the weirdest behavior to identify. If it is all exposed and usable (seems to be), just bear that in mind if you encounter issues with your setup to pull non-matching RAM out first (try original set, then the other).

I think you would be better off using the 2 1gb sticks without the two 500mb sticks.

Grem
I think you would be better off using the 2 1gb sticks without the two 500mb sticks.

That's kinda what I figured.
Thanks, everyone.