Can I install a new arm on this old table?

The KD-500 came with two circular cut outs for installing a tonearm. One was drilled with a concentric hole, the other was an SME slot. (You'll probably want to use the circular hole.) It should be a simple matter to attach a new arm, provided you have the instructions and fittings that presumably came in a package with the new arm.
It shouldn't be any more difficult than attaching and fitting a cartridge, and no soldering should be necessary.

Thanks for the reply! How do I know which arms will work and which ones won't? Recommendations?

A Rega should work and would be a good choice. You'll have to use spacers to adjust the height. With this tagle I wouldn't spend too much on an arm - maybe you could look here for a used one.

Brusson: thanks for your help, much appreciated. I found an RB300 for less than $200, which is on its way. Do you know where one can find these spacers you speak of, and how they're used?

Also, I'll be looking for a cheap MM cartridge. Suggestions?

Thanks!