Hello,
By default, some of the resources our ASP.NET controls are using are embedded inside the DLL assembly and accessed by the built-in ASP.NET WebResource.axd HTTP handler. One such typical resource is the javascript client-side file, or some of the default CSS files/skins, some images, etc.
It is really very weird that you have these types of errors. I have some suggestions though. Once I was working on a project and had similar symptoms - they were related to the Elmah error logging module (a very popular error log module). Are you by any chance using Elmah or a similar error logging module?
Also, some more information (for example raw lines from the logs generating 404s will certainly provide additional clues.