Google limits the list of fetch errors to 1000 per day. There is almost nothing you can do about this.
I cannot tell you why you are getting so many 404 errors.
If you can fix the problem, then you will be able to Mark as Fixed these 404s to remove from the list 1000 per day. But I would only do that if you really need to see any additional errors and you do not have another way to assess broken links on your site. Otherwise, I do not recommend tying to Mark as Fixed any 404 error unless you absolutely know that the page does in fact work correctly.
You can use http://www.screamingfrog.co.uk/seo-spider/ to find any broken links for your site. It is far more efficient and will give a complete list. Screaming Frog does require a license for more than 500 pages, but it is affordable and an excellent tool! Most people opt for this tool to help keep their site healthy. It can help you identify exactly where these broken links are. You should be able to see a pattern this way and hopefully find the original problem.