To make search show only open tickets in the basic search:
include/staff/tickets.inc.php
Remove:
if(!$search)
--
This forces the search to default to 'open' unless the case() above it matches other criteria. Makes things much simpler to remove the closed tickets from view. This might be a cool preference feature for the user to be able to specify what he wants by default in searches.
You can also update the following lines to default 'open' in the advanced search so you don't have to specify it every time.
297
298 Any status
299 >Open
300 ...
