Although Google Webmaster Tools analyzes your website from the perspective of the Google search engine rather that visitor activity that occurs directly on your site, it does provide critical information that can help you drive more traffic to the correct pages on your site, thereby improving visitor experience and possibly increasing conversions.
Within the Health > Crawl Errors report, you can view broken inbound links that the Google search engine spider (“Googlebot”) has encountered, and the external pages that contain the broken links. You could further assess the impact of the broken link by drilling down in the Referral Traffic report within Google Analytics for the number of visits that the external pages are driving. (This is possible only if you have included the Google Analytics tracking code on a custom page-not-found page, which is highly recommended as part of your Google Analytics implementation.)
Fixing the broken link can benefit you in two ways. For one, it can help direct more visitors to the correct pages on your site instead of an error page. Secondly, it can potentially improve your organic rankings within Google, thereby driving more traffic.
Read more about the ways that Google Webmaster Tools complements Google Analytics.