Several users in the Windows Live Writer forums have reported seeing “Error 400: Bad Request” when publishing to Blogger with images:
This happens when some values are missing from your Windows registry—specifically, the content types of .jpg, .gif, and/or .png extensions. I don’t know exactly how they are getting removed, but it’s almost certainly a buggy uninstaller from some other application.
In any case, you can fix this problem by running this .reg file. No need to reboot or restart Writer.