Search engines don’t like broken links because they think that you are not maintaining your website.
Going back and correcting these links is good website maintenance.
How do you find broken links?
There are several tools out on the market as well as you can set up Google Webmaster Tools and it will tell you.
Once they have done a scan of the website, they will give you the page and the link that is broken. Usually you will get a download into an Excel file.
Just go into the CMS and correct the link.
Do you have a favorite tool for checking your links?