I'd personally go with some server-side log analyzers for continuous monitoring of dead links.
Webalizer/Awstats and probably other tools can give you a report of any 404 Not Found errors by parsing your webserver log.
Advantage of this approach: You also catch incorrect links to your site which might be posted on some other site, user typos and so on. And it's continuous monitoring, not just one time when you run some dead link checker.
You can combine this with a website mirroring software like httrack. Just have it crawl your site and then get the report from one of the log parsing tools.
There are also some desktop apps which can parse apache log files and give you any 404 errors in a nice report.