I would really like to see a function like this developed into MediaWiki, either an an extension or into a new version. Put simply, one should be able to perform searches, limiting the field of search to articles in a given category. The reasons why this would be useful are probably obvious. If not - the simplest one is just that categories split articles into topics - and this would allow a user to search in a given topic.
I see two ways of enacting this, and I think both should be looked into. Firstly, an "advanced search" option, which I think is not as favourable. Secondly, and this is what I think would really be good, a search box automatically appears on a category page.
Alternatively, when one is viewing a category page, the normal search box (on the left) acquires a check box - "search in this category".
Additionally, a further checkbox could be interesting: "also search subcategories".
I can't imagine this would be too difficult to implement, but would certainly be very useful and would make more use of the categorisation system in MediaWiki.