One of the first strategies we attack with clients when it comes to search engine optimization is errors in Google Search Console. While I can't quantify the impact of errors I can tell you that, without a doubt, our clients with the lowest error counts in Webmasters have the greatest SEO rankings and organic impact.
If you're not using Google Search Console on a regular basis, you really should be. With some clients, we pay much more attention to Webmasters data than we do with Analytics itself!
Improving click-through rates, improving ranking and pagespeed is a complex issue, but errors are much easier. Errors send a message to Google that your site isn't too reliable. Google doesn't want to send users to pages that are not found or a site that is not consistantly a source of fast, relevant, recent and frequent information.
Managing redirects to take searchers from pages that no longer exist to pages that do isn't just great for your search engine optimization, it's also absolutely critical to provide visitors with a valid page. They may be clicking an old link on an external site, or they may be clicking a search result… either way, they were looking for something on your site. If they don't find it, they may just abandon and go to the next link, which could be your competitor.
If you're using WordPress, an easy way to do this is to simply add an array of redirects within your 404 page template!