Hey There
Google's webmaster documentation says;
"Generally, 404 errors don’t impact your site’s ranking in Google, and you can safely ignore them."
When Google says "generally" this tends to mean "in most cases" or "not directly" or "there may be secondary effects"... you get the idea. 
But I think they are assuming you need to be smart enough to know if the 404 was intentional, and if not why it happened. For example - if you had a really popular piece of content with back links directly to that URL, and then the URL 404s - you supposed may lose the "link juice" pointing into that article. So in that regard 404s can hurt rankings secondarily.
But as other have said, you can redirect your 404s to a similar page (Google recommends not the homepage).
I am not sure why the Moz report puts them in "high priority" - perhaps they mean "high priority" from a general web best practice point of view, and not strictly SEO.