If you try to issue a "mt.getCategoryList" or "metaweblog.getCategories" call via the blog module, you'll receive a cryptic error:
"Blog API module is not configured to support the blog content type, or you don't have sufficient permissions to post this type of content."
What's happening is the blogapi_metaweblog_get_category_list method is running the "must be authorized for content type" test, but not running the user login test first. It seems that it just fails to authenticate in this scenario.
If you add the user content test first, then it works. Patch attached.