Ahemp, above I wrote "wineserver" (run it only once, or otherwise you'll get another error when running "wine" later). It's actually "wine" that must not be run more than once, and since "wineinstall" invokes it, after each failed attempt to compile it you need to restart Fedora, type "wineserver" and then "wineinstall".
Now, some more help:
The updated Fedora 3 FAQ does things a bit differently to disable exec-shield.
This is from the current recently updated (after my last post) FAQ at http://www.fedorafaq.org:
13. Q: How do I get Wine to work?
Edit /etc/sysconfig/prelink. You'll need to change:
Then do this to disable exec-shield:
prelink -am --no-exec-shield
You might want to try it this way, to see if it stops to segfault.
I currently don't have the opportunity to try it, but will do it later.