The mobile version of our site is m.example.com. We followed all the recommendations on https://developers.google.com/webmasters/smartphone-sites/details which include having a canonical from mobile -> desktop and rel="alternate" from desktop ->mobile
Recently I started seeing on Google analytics more traffic coming from Google to the mobile site but from visitors who are clearly not mobile (Windows OS with large screen resolution). I dug deeper and found out our mobile site is appearing on desktop search results for certain queries. I was under the impression that having a canonical tag from the mobile page to the desktop version should eliminate that option.
I currently have an auto redirect from desktop -> mobile for mobile users but not the other way around, meaning you can access the mobile site from a desktop. Should I implement the redirect on the other direction as well?
We had a similar problem but it was because of a ?url.string to deactivate mobile. It sounds like you've got your bases covered though if you've added rel-canonical. Our solution was "URL Parameters" in GWT but I wouldn't use a redirect to move desktops and mobile devices around to the proper sites.
I'm not certain if you'd get dinged for redirecting just Gbot from your mobile subdomain to main domain but it's what I'd look into.