You do not need a custom error document in order to monitor 404's on your site - if that is the requirement. All the information is in your server access log. The HTTP response code (ie. 404, 403, 200, etc) and the URL of the request that produced that response.
The custom error document is a nice way of serving a meaningful response to users.
You can also register your site with Google Webmaster Tools (GWT). This will produce a report of all the URLs that it attempted to crawl (ie. URLs that it could find) that produced a 404.
Bare in mind that your access log will report a lot more 404s than GWT because there are a lot of nasty bots out there looking for vulnerabilities that will try to request all sorts of URLs that might be unrelated to your site. Ignore these, or block the bots if they are persistent.