Hi Alex,
Without diving in to the issue of increased number of 404 errors being reported by Webmaster tools account, let us first look at the core issue where, 404 pages (non-existing resources) that return an HTTP header status code 200. These are called, 'soft 404 errors'. Ideally all the non-existing resources on the website should return an HTTP header status code 404 or 410 as per the situation and not a status 200 which is very confusing for search engines and a bad practice. This should be fixed immediately. Please have all such pages return 404 and not 200 as soon as possible.
Here you go for more about the soft 404 errors:
https://support.google.com/webmasters/answer/181708?hl=en
and here to know more about when to return a 404 status code:
https://support.google.com/webmasters/answer/2409439?hl=en
Best regards,
Devanur Rafi.