Those error messages are normal. You should get a nice little winecfg window in a few minutes, after it creates a new .wine folder. Perhaps you have messed up the permissions in your home folder. No matter, remove the old .wine and re-run winecfg.
If you upgraded to FC6 from FC5, your yum is out of date:
Go into the /etc/yum.repos.d and edit the repos, enable only core, extras and updates.
yum clean all
yum update yum
Yum is now fixed up, just like as if you installed fresh...
Optionally go to http://livna.org
and download their rpm for "using livna"
Remove the old wine and install wine through yum, e.g.
yum remove wine*
or the more dangerous command:
rpm -qa |grep wine |xargs rpm -e
yum update -y
yum install wine* -y
All correct and good to go. Fedora is just a collection of files. If this doesn't work, maybe you got hardware issues...
Some useful links for debugging rpm-based systems:
Maximum RPM Chapter 6 (should probably read the whole thing someday)
Oh, and don't run wine as root.