I'm active on several StackExchange sites, and a moderator on two of them. With the increasing number of SE sites it's getting more complicated to keep an eye on the stuff I'm interested in. The stackexchange.com tag filters are a good start to be able to monitor several sites at once, but they can't yet replace visiting the main SE sites.
The important stuff I'm missing when I only look at a tag filter on stackexchange.com are
- flags on sites I moderate
- suggested edits
and the not so important, but nice-to-have stuff that is missing is
- question information like number of votes and views
I tried already to use tag filters to monitor my favorite sites but they just can't replace visiting the sites themselves yet, especially for a moderator. The part I absolutely need so that tag filters could serve as a standard way to keep track of my sites are flag counts. At the moment I'd still need to regularly check on the site itself to see if there are any flags, making the tag filters far less useful to me than they could be.
My subjective impression is that the way people use the SE network varies a great deal between users, so I doubt that there can be a one-size-fits-all solution to this. For example the SO mods probably would not want to have the flag number displayed anywhere else, they don't have to check SO itself to know that there are lots of flags, there are always flags there.
Ideally, visiting stackexchange.com should be enough to see all the relevant information for me for the sites I'm interested in and the sites I moderate. It might make sense to make the site more configurable, to allow users to select what they want to monitor and customize the site even beyond just tag filters.