A 503 error is a service unavailable error. I have seen situations where redirects are incorrect and loop. Depending on the hosting setup, this can trigger various HTTP error codes.
The best way to debug this is by looking at your Apache access logs. Scan your logs for the 503 errors. Pay attention to the URL being requested as well as the referring URL.
Very likely, there's some looping process and in cases when Apache runs on FastCGI, you can get a 503 error due to too many processes being triggered.
Also, due to how WP handles 404's, I've seen many plugins mask underlying causes. So if you have any plugins that impact error handling, you may need to remove those while debugging.
You can also use http://www.redbot.org/ to check the headers for any page that should be redirected. That tool should return a Location header with a URL. Visit that Location URL in your browser and make sure it resolves.
The goal here is to try to replicate the behavior. Once you can replicate the behavior, dig into your redirect/rewrite rules and examine the logic to determine why you are seeing the loops or failures.