The application layer, the part responsible for responding to API calls, page views, and so on, directs requests to /services/Soap/class/ to an appropriate handler that loads the application binary for that class (much like the Java Class Loader loads classes) and translates the parameters from XML to native objects, runs the code, and handles the translation back from native objects to XML.
The internal logging systems will record every request, even those that fail, and several class of employees have access to some version of the logs. However, depending on when the call fails, you might not have access to those logs. For example, if you don't have a session header, then there's no way you could possibly log that on the salesforce.com end.
In fact, it seems like anything that causes an error before the transaction starts never reaches the client-level logging system. For assistance with SOAP problems where you can't even get a log, you'll need to contact Developer Support, or ask a specific question here on SFSE. We'll do our best to help you out. Also, consider using a SOAP client like SOAPClient.com against your WSDL and see what happens.
If you need to ask a question here, be sure to include a (redacted) sample of your SOAP request and response, and possibly even the relevant part of your WSDL, plus the exact error message. The more information we have, the better we can help assist you.