So I go over to a stock rh7.1 box,
compile my serial port application.  Run it, it fails
since I don't have privileges to /dev/ttyS0.

I'd normally do a:
su -
chmod u+s /dev/ttyS0
or
chmod u+s serial_prog

Problem is that this lets everybody have root privileges.
I would guess that a better way would be to make me
part of the select group that has privileges to /dev/ttyS0.

ls -l /dev/ttyS0
crw-rw----   root uucp .......

Say I have a UID of "karl", apparently I default to
being my own group named "karl".

So how do I make user karl be a part of the uucp group?
I assume then I would be able to use the port.