Kibana 4 as reverse proxy

ProxyPass /kibana http://localhost:5601/kibana
ProxyPassReverse /kibana http://localhost:5601/kibana

I think you want to have trailing slashes here, and more importantly no kibana directory on the right hand side:

ProxyPass /kibana/ http://localhost:5601/
ProxyPassReverse /kibana/ http://localhost:5601/

Without the trailing slashes, relative URLs tend to get screwed up. The debugging console of your browser will indicate such problems quite clearly.