Although both the luke and core admin handlers set http caching to false in the response headers** I believe the Cache-Control settings are ignored during ajax requests in certain browsers. This can be a problem if you're refreshing admin to get the latest do count. It can also be a problem when you compare the count of "Num Docs" on the main index page (/solr/#/CORE) vs the count on the core admin page (/solr/#/~cores/CORE). Consider that if you first visit the main index page, add and commit 100 docs, and then visit core admin the doc count will be off by 100.
If this is an issue the ajax requests can explictly set caching to false ( http://api.jquery.com/jQuery.ajax/#jQuery-ajax-settings ) ... for example, inserting 'cache: false,' after line 91 here: https://github.com/apache/lucene-solr/blob/branch_4x/solr/webapp/web/js/scripts/dashboard.js#L91
Tested using Chrome Version 24.0.1312.52