Before, we would use the site health in the analytics area to check 404 error reports. This has been removed in 8.2, so what is the expected way to get this information?
In terms of what we are supposed to do now, I'm not sure. As for the Site Health, it's still there but it has been hidden. There is a tutorial on how to get it back. http://blogs.benjaminvidal.net/posts/2015/enabling-engagement-analytics-in-sitecore-8/
And also, how to trigger the 404 reporting http://blogs.benjaminvidal.net/posts/2015/sitecore8-site-health-reports-not-found-urls-report/
