A typical page reference on our Wiki is "http://daytonlxdev3.oneilinc.net/cgi-bin/wiki/wiki/4".
The second 'wiki' is the CGI script. When I go to the "References To ..." page,
the URLs for all links change to this: http://daytonlxdev3.oneilinc.net/cgi-bin/wiki/4.
I'm using the latest versions of Tclkit and Wikit. I've attached the CGI script
that runs everything, in case it's causing the problem.

This is a tricky issue - I believe the workaround is to define a WIKIT_BASE
environment variable in the CGI script, *with* a trailing slash. In your case probably:
WIKIT_BASE=http://daytonlxdev3.oneilinc.net/cgi-bin/wiki/wiki/
-jcw