Similar to https://phabricator.wikimedia.org/T86040 reported for the Add Template inspector:
Seen in Chrome and Firefox. Note that behavior in Chromium (at least on my OSX laptop) seems OK.
On any page in beta labs e.g. http://en.wikipedia.beta.wmflabs.org/wiki/0.9753751036924678?veaction=edit
textbox for search input should have focus
default search text in textbox should be highlighted
such that with no other action, loading the Media inspector and hitting RETURN should clear the search input textbox completely in preparation for typing