So after all the trouble I had with PiPlay, I looked to see if there were other Pi-Mame projects out there. The first one I found, after PiPlay, of course, was this one. By comparison, everything is better with this.

https://code.google.com/p/mame4all-pi/

The install is super easy -- you just download it and unzip it on your Raspian desktop, then place it where you want it. No need to make an SD-card image (Thanks for having me go through that learning experience. It was great. Seiously, i learned a lot). Granted, it's not stand-alone, so you can't just leave it running for people to use, like an arcade.

It's much faster -- all of the games that ran slowly or not at all with PiPlay worked with this.

The Colors are correct -- Piplay had issues with some colors, even when you switched to high color modes.

The Folder structure of it is just like PC-based Mame, and you just dump the ROM zips into the ROMS folder, artwork
into the artwork folder, and so on.

I was starting to think that my SD card was defective or something, after my experiences with PiPlay, but I am using the same SD card with a fresh copy of Raspian, and it works fine.