To a certain extent you've got this already.
If a user's got to 10K there's a pretty good chance they're going to have a silver or possibly a gold tag badge (or two). By the time they're at 20K they'll almost certainly have. At that level they have access to the tools menu where they can see questions with close and delete votes and also the posts that have been flagged.
They can add their close votes from these lists rather than having to search questions and they can still flag posts for moderator attention if there's something particularly bad. These users will, by definition, be concentrating on question in their favourite tags.
Moderators get to know who the good flaggers are. It's easier on smaller sites, but even on SO I expect you'll see certain names and think "Ah, X has flagged this - I'll just close/delete/whatever". There'll be some checking, but you know it's a "good" flag.
Agreed, the close doesn't happen straight away, but it does happen and probably more quickly than if left to the rest of the community to stumble across the question and vote.