Please make sure the search is fuzzy! Using a similar algorithm to Xcode would be great, but hopefully one that doesn't break as much.
Personally I don't think filtering is necessary, but it certainly shouldn't be enabled by default. Users can hardly be expected to keep up with deprecations and will wonder where the APIs they see on StackOverflow or these forums aren't coming up in the results. I would like to see deprecated symbols in their own section of the list, like we see in Dash.
More generally, a section in the sidebar for inherited or protocol conformance APIs would be great too. Such a pain in Xcode and Dash that I have to remember that certain things live on UIControl and not UIButton. It would also be nice to separate out my View's specific APIs from the billion that we inherit from View, while still letting us view those APIs if we want.