Has the spam problem declined a lot since the new reviewing interface (or the badge) was introduced? I have hardly flagged anything as spam or "not an answer" since then, and not because I'd recently gotten the Marshal badge and could rest on my laurels or something. Are more people reviewing now? Is this something the underlying data can reveal?
An unconditional Yes.
We are seeing significantly more editing and improved voting.
The new "close" tab in
/review also increased the amount of closing. And we are seeing more bad content get deleted.
I also had some more stats about review at: Is the marked state for reviewed questions bleeding across to late answers?
The increase answer deletion does directly correlate with us catching more spam and bad answers.
We are seeing close to 4000 reviews a day all by users that have
Strunk & White.
Bottom line, content is getting more improvements, people are participating more in janitorial work. Only big pain point is that we need a few more mods on SO, something that will be solved by the election.