It's your feedback links too. Check out your conf/_config.php file and see what you have for $baseurl. I got this feeling it's the old domain.

Thanks SuperGuru! Now do you think I should upgrade? I don't want to risk fixing something that isn't broken.

Yup. Just because it's not broken doesn't mean it's repairable going forward Support for 0.9.* stuff is rare as hen's teeth because no one who answers questions runs it anymore. Besides upgrading to at least 1.8.7 will give you tons more flexibility in what you could do if you wanted to. Click 'extend' (above) then 'plugins' to see what's not going to happen in 0.9.* for example. I run 3 installations. One of them is still on 1.8.7 so that's gonna get upgraded to 1.9.2 tomorrow morning. Finally. After that all three get upgraded to 1.9.3 because they are heavily modified and I don't want them becoming impossible to deal with down the road.

Backup your files and database before you begin, upgrade per the instructions, and be prepared to give it an hour to get it working smooth again. Your skin might take quite a bit longer than that because there have been tons of changes in how skins make your blog happen, but any custom skin can be brought forward with a bit of careful comparison and thought.