Yes, it should replace the old URL with the one that it redirects to.
Perhaps you have an old version of CURL that doesn’t properly handle redirects? Click “Show debug info” in Settings -> Link Checker and check the displayed table for redirect-related warnings.
My only warning there is that I use open_basedir. I administrate this server, so I can make the server changes as they need be made.
GFM
Hmm, so what happens when you use the “Fix redirects” action? Is there an error message, or does it say it fixed them without actually doing anything?
Another thing you could do is verify that the plugin is correctly detecting the redirected-to URL. To do that, click the “Details” link of one of the listed redirects and check the “Final URL” value. It should be different from the original URL.
The plugin appears to be seeing the correct URL on the destination of the redirect, but using “Fix Redirects” leaves the link unchanged.
GFM
Have you already updated to the latest version (0.9.5)? Also, could you post the HTML that corresponds to the problematic link? Maybe there’s something in the link code that confuses the editing routine.
The post HTML looks fine, but that isn’t saying much. WP applies a number of automatic transformations to post content before displaying it, so the HTML that I see at that link can be entirely different from what shows up in your editor and is stored in the database (and thus seen by BLC).
Try this debug version. It will output a number of status messages when you use the “Fix redirects” option, which should provide some clues as to why the redirect doesn’t get fixed. Post those messages here.