I'll pay someone $50 to make a plug-in that will replace WordPress's search with a search that looks at the categories a post belongs to.
To be clear, if a post belongs to the categories: fun, work, and home, and I search for "fun work" or "fun, work" this post will come up. If I search for "fun, work, food" this post will not come up. If I search for "work, home" this post will come up.
Also, the query can be in a different order. If the post belongs to categories fun, work, and home... then searching for "fun home" or "home, work" or "work fun" should return that post as well.
This shouldn't need a ton of explanation. It follows the same logic as a tag search on any major site using tagging. Let me know if you're interested.