Google show you 404 error report so you can know the list of pages is not found by Googlebot while crawling other pages. 404 Does not harm your site at all, but you can make it better by checking how they find links.
When to fix 404 error?
Let's say you have changed your site structure and your URL is slietly change, now if you see that kind of 404 error then do 301 redirection, because it is helpful for users as well as for bots. When you do 301 redirection, then PageRank is also passed on that link, it means you page URL position in search result will be same even after you change your site url structure.
When to not fix 404 error?
Now if you see 404 error page, because some bad/low/dead website point to your site URL, then you don't need to do any redirection. Even that kind of 10k links does not affect your site at all.
Google know that, webmaster should not waste their time by fixing bad links. So it does not hurt your site at all. Just leave that, it will disappear automatically after few months.