I just installed Contact Form 7 (version 3.5) to my development website today, and am also getting the spinning arrow. Eventually, if I leave it for awhile, it sends the email, but it takes a long time (like an hour or so). I just installed Contact Form 7 today - and it installed the latest version.
Interestingly, though, I had the old version of Contact Form 7 (version 3.4.2) on another website. I also updated it to the new version today, but appears to be working fine. It's not getting the spinning arrow nor is it taking forever to send an email.