How to filter content by taxonomy term?
It is easy to expose taxonomy term as filter in views. Unfortunately, in Drupal 7, the content list is not built by views.

Administration Views is a module which can replace it with the views Administration: Nodes.



In the views, you can add Content: Has taxonomy term filter and expose it. But it only support ONE vocabulary.



How about having a term filter on more then vocabulary? It is quite tricky, but not impossible.

First, add a relationship Content: Taxonomy terms on node, and check the vocabularies. In example, they are tags and topics.



Then, now you can add filter Taxonomy term: Name, this filter only appear when you added the taxonomy term as relationship.



In Operator, there are many options, you can pick a suitable one for your case. I chose Contains in my example.




  Note:
  
  With this method, you will have a ordinary text field rather then autocomplete field. It is the only downside.