The error you're seeing is because HTTP is made up of many different types of requests. One you already know--GET--and others--such as POST--you probably recognize. A full list is available. Basically, depending on the file being accessed, certain request methods are allowed--in this case, it looks like only GET is expected, and its receiving something else.
This could be due to a variety of issues. Most likely, a plugin--either for Apache or Wordpress--is getting in the way; try disabling any low-level plugins that deal with caching, compressing, etc., and see if you continue to see those errors. For example, WP Total Cache (on the WP side), and mod_pagespeed (on the Apache side).
Let me know if you continue to encounter errors.