I've tested the plugin pretty extensively on 3.5.1, but I may have missed something.
I just released a new version, so could you confirm that the new version still doesn't work? I didn't do any specific fixes for 3.5 in the new release, but it's still worth a try.
If it's still broken, could you log into SendGrid and go here: http://sendgrid.com/logs/index
Do the emails show up there? Do they show as "Delivered", or something else?
If all else fails, could you try disabling any other plugins, and enabling the default theme? If that fixes the problem, one of your plugins, or your theme, is interfering with WP SendGrid.