I'm using WP 3.4.2 in a multisite installation with a combination of subdirectories, subdomains and domains. It works in at least one of the subdomains, but not in the subdirectories or in the root blog.
One thing I noticed that at least made it behave differently, in wp-admin/js/set-post-thumbnail.js Firebug was showing this line:
action:"set-post-thumbnail", post_id: post_id, thumbnail_id: id, _ajax_nonce: nonce, cookie: encodeURIComponent(document.cookie)
In the key value pair "post_id: post_id" it was interpreting the key as a variable instead of a string, so it was passing something like "71: 71". I put quotes around the key, so now I see that the POST is actually populated the way it should be -- it was empty before -- but still the server isn't responding.
Here's the form data sent to admin-ajax.php: