Will a large percentage of 404 links negatively impact SERP performance?

[DirectiveGroup]

We discovered a broken link and issue with a dynamically generated sitemap that resulted in 9,000+ pages of duplicate content (namely there was not actual 404 page, but content for a 404 page that populated on the broken page).

We've corrected that issue so the 404 page is working correctly now and there aren't any more broken links on the site. However, we just reviewed our Google crawl report, and saw that now there are 9,000+ 404 links in the Google index.

We discovered the initial error when our SERP performance dropped 60% in a month.

Now that we've corrected all the duplicate content pages, will vast number of 404 pages negatively impact SERP results? If so, do you recommend doing 301 redirects to the page it should have gone to, and do you know of any automated tools performing the 301's (it's a standard HTML site, no CMS involved).

Thanks for your help!

[DirectiveGroup]

Thanks for your response. Does it seem probable that this issue caused the 60% drop in SERP performance? The only other variable near the same time was changing hosting providers. We have moved to this provider for other clients, and never saw this kind of change, but that was usually at the beginning of the SEO campaign, not in the middle.

[Malarowski]

Give it a bit of time and it should fix itself. Google will crawl it and find that it is no longer broken.