ZydoSEO - 3:27 am on Feb 28, 2013 (gmt 0)
I'm not sure what platform you run on (Windows/IIS or Linux/Apache) but your web server logs are a great place to monitor for 404 errors (not to mention tons of other "stuff").
WMT has a delay before problems are reported, and I doubt that every 404 that occurs on your site is logged there. Users may be clicking on broken links days before Google crawls a broken link.
If your site's hosted on an IIS platform and you have access to the logs, Microsoft has a great utility that you can download for free call Log Parser that allows you to query IIS logs using SQL statements. It's actually pretty sweet. If you're on Apache, I'm not sure what utilities they might have that are similar... I guess there's always grep! ;)
It probably wouldn't be a bad idea to crawl the site w/ Xenu Sleuthe or some other utility to get a list of any broken links.