I’m using CF7 3.3.2 and WP 3.4.2
I’ve been troubleshooting this problem myself – spinning icon, email sends, and then no confirmation on the page. As it turns out, I was using the old Analytics tracking code in the “Additional Settings” box of my contact forms (in order to do virtual URL tracking for my goals when a user submits the form).
If you have a line of code in the “Additional Settings” box (when editing your CF7 form) beginning with “on_sent_ok” and it has “pageTracker” in it, you’re probably using the old version of the tracking code.
You can see more details here:
http://contactform7.com/tracking-form-submissions-with-google-analytics/