I just figured out what is going on..
But first, I looked at the two earlier reports about the message.
You probably know this already, but for the sake of this documentation, I think I should make it clear how the '400 bad request' appear.
The Bad request message shows up instead of minified CSS, which is why people complain that the CSS is broken. It is not there.
For example, when it calls to minimize some of the CSS files, when looking at the 'CSS code' supposedly produced by the BWP minify URL showing in the html, rather than minified CSS, it instead has this message as its sole content:
<h1>400 Bad Request</h1><p>Please see http://code.google.com/p/minify/wiki/Debugging.</p>
This message is from 'min/builder/index.php'.
Solution in my case:
Checking around in other logs I found, that it was a conflict with the the cache plugin, in my case WP Super Cache, using a CDN.
Along the way, the cache plugin decides to manipulate the CSS/JS URLs calling on bwp-minify, and redirect them to the CDN, adding another host and directory prefix.. The '400 Bad Request' was coming from 'min', because the directory structure "over there on the CDN" is not what it expects, now with a prefix added to the path.
Adding another filter string to the cache plugin, telling it to stay away from URLs that has bwp-minify in them fixed it. Now bwp-minify calls stay off the CDN.