I really need to be able to exclude tickets in statuses closed, resolved, awaiting input, and QA from my search results.
There are are some advance searching techniques that may help you define more specific searches. Below are a couple links that may be useful.
Tutorial: Understanding Advanced Search and Syntax Rules
Advanced Search Options
However, if you are looking to find incidents in a particular state or incidents excluding certain states. I would recommend filtering from the incident queue. You can filter by 'State' or by 'State is Not'. You can add multiple filters to help refine even further. Once you have the filtered down for the incidents you're looking for, you can save that report so that you can quickly pull it up anytime as opposed to filtering again every time you need to view those types of incidents.
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