If you pass the Mobile-Friendly Test tool, then Google will take that into account. Besides that there is no real method other than go to Webmaster Tools >> Crawl >> Fetch as Google >> Fetch & Render [desktop & mobile, just to be safe] >> Submit to Index.
Unfortunately, currently there's no way to manually get rid of the old errors in the Mobile Usability section. They'll eventually disappear once new data gets imported.
Once again, you can simply search for your page in Google using a mobile device, and if your page has been crawled after passing the mobile test, then it should show the "Mobile-friendly" tag in the result snippet:
Seeing that tag means that Google considers your page to be mobile-friendly, so you shouldn't worry about the outdated information that you see in your Search Console.
Hopefully, we'll soon either see a faster update frequency of the information or use new features that will allow us to hide/remove/"mark as fixed" outdated data.