I’ve looked through the code in /wp-includes/comment.php but – to be completely honest – I still have no clue as to what the root cause of the error is.
On the surface, the problem is that the pingback-related stuff in comment.php can’t handle URLs that return multiple ‘Content-Type’ headers. This is not surprising as, in general, no reasonable server returns more than one HTTP header of this type at a time.
How this relates to Broken Link Checker I have no idea. The plugin doesn’t mess with headers sent. It doesn’t even contain the text ‘Content-Type’ anywhere in it’s source code. The bug, whatever it is, must be something extremely obscure.
As for redirects, I’m guessing that your server doesn’t have the Curl library installed. Without it, the plugin can’t detect redirects. Check the “Show debug info” thingy on the settings page to verify.