I can describe my big desire, as a power user and an expert in some cross-site areas: discoverability and manageability of communities and questions, preferably without needing to be actually on the network at all times.
It's not a feature request, at least in its present form, but:
The cross-site Filtered Questions on Stack Exchange are a bit awkward to use, making site and question discovery extremely difficultThe cross-site Filtered Questions on Stack Exchange are a bit awkward to use, making site and question discovery extremely difficult
It would be nice to have better discovery tools. There are a lot of sites in the network. Just looking at my professional interests, I can answer questions across over half a dozen sites.
This fits in with your filtering stuff that was mentioned in the question, but being able to put the right communities and the right questions in front of the experts is only beneficial. Ideally, you'd see higher quality answers to questions.
Something tangentially related to filtering and discovery:
Additional RSS feedsAdditional RSS feeds
As long as you aren't as aggressive in blocking feed readers as Reddit is (my Reddit feeds in Feedly rarely get updated because Feedly hits the Reddit rate limits and Reddit refuses to increase their allocation), RSS feeds can lead to some interesting discovery, data analysis in a closer-to-real-time situation, and integrations with third party tools (using something like IFTTT or custom software).