How can I list all the StumbleUpon reviews for a certain site, such as webapps.stackexchange.com?
In short, the answer would have to be... No.
We offer some tools along these lines, to those interested in promoting their sites, via our StumbleUpon Advertising programm
- CH, StumbleUpon employee
Not unless you sign up with their Paid Discovery plan which should give you analytics for all the pages under your site(s) that have been stumbled.
Looks like it's a way for them to offer an upsell on the StumbleUpon service.
Otherwise, comb through your logs for something with stumbleupon in the referrer URLs.
Another painstaking way to to append each URL to http://stumbleupon.com/url/ and collate the results yourself.