This Broken Link Checker Plugin by Janis Elsts will check your posts, comments and other content for broken links and missing images- and notify you if any are found.
A very handy tool!
Download the version that was available when we wrote this post here:broken-link-checker.1.8
For updates, support and to check if you have the latest version Click here.
Here is another Link Checker tool for checking links externally, which explains why you need to stay on top of this – but we use & love Broken link Checker Plugin right in the WP dashboard.
NOTE: Google really dislikes broken links.