Care you explain how you would do that search on, say, redmine.org? AFAIK, you can search descriptions using the search box in the top right, but you can't filter those results by status or category. In the issues list, you can create a filter for status and category, but not description.
It would also be nice if you could search for attached files. There have been times where we have a file and can't find the bug associated with. I have to open our MySQL instance and look it up there.
You can't search for multiple works in the subject. For example, if you filter the open issues of redmine.org for subjects with "email asynchronous", you don't get any results. Filter for "asynchronous email" and you get at least one result.
Redmine is nice (especially the REST API), but its search sucks.