Moving to a new URL?

I just changed the URL of my WordPress installation and everything’s working fine except for a odd login bug. I used to stick to the sidebar login widget for quick access to the dashboard, but ever since I switched URLs, I’ll have to login again after clicking the dashboard link. Normally I’d think this was a problem with the plugin itself, but it seems that the dashboard page won’t save my password on its own either.

I’ve got this sinking feeling that the problem is caused by my new domain name, which is still set up as a redirect while I work on switching out all the posts which have their links hardcoded, which resulted in maybe a mismatched cookie which is still referencing the subdomain? I’m probably way off with that theory (I’m horrible with cookies, even in concept), but I may as well cover my bases, which leads into the next question.

As I already mentioned, the other author on the blog has this habit of hardcoding their links, so all their posts are now referencing the subdomain instead of the new domain. My question is, would it be possible to use the export tool, replace the text in a text editor, and import without any problems, or would it result in something like duplicate entries?

And those are my two questions. I’m not too worried about the first, but any help regarding the second matter would be very much appreciated! Thank you!