This could also be the result of mixing Apache 2.2 directives like Order and Satisfy with Apache 2.4 directives like Require. The old directives are supplied by the module http://httpd.apache.org/docs/2.4/mod/mod_access_compat.html and since the errors you were seeing in the logs were from access_compat perhaps those would also go away if you avoided using those directives altogether. I only just now stumbled across http://httpd.apache.org/docs/2.4/upgrading.html which mentions changing from 2.2. to 2.4 but the examples it gave did not show our use case:
Order allow,deny
Satisfy Any
So I don’t know what the corresponding Require directive for this would be. Since there is already Require valid-user is it possible to just remove those last two directives?
Though it looks like you already found a workable solution - just ignore those errors.