*) Keyboard is not reliable (or working at all)
*) Mouse is not reliable (or working at all)
*) Random kernel panics
*) Errors reading SD card
I swapped in lots of different keyboards and mice. That didn't help. I tried many of the available distributions, and a wide variety of SD cards. That didn't help.
As I did more and more reading, I took the advice listed on this page:
http://elinux.org/RPi_Hardware#Power
I had been using two different phone chargers. One I knew was cheap, and the other should have been decent. I finally switched to my iPhone charger, which I trust is a quality item.
Using a good quality power supply is a must. That fixed all my random kernel panics. And then to get a reliable keyboard and mouse, I am using a powered USB hub. Don't ignore power requirements on these little machines. Once I got my power woes sorted out, I'm having a MUCH better experience.