When I end up in this situation, I turn to a little-known but incredibly powerful tool from Microsoft called Fiddler. Fiddler is an HTTP debugging proxy that filters all the requests coming to your machine via HTTP. It interfaces directly with WinINET, the Microsoft Internet communications stack, so it automatically picks up any requests and responses by programs using this library. By simply starting Fiddler, it will automatically pick up HTTP traffic for Internet Explorer, Safari, and Opera. Firefox doesn't use WinINET, so you need to manually set it up to go through Fiddler. You can do so by going to the Tools menu and clicking on Options. Go to the Network tab and click the Settings button. Select Manual Proxy Configuration and enter localhost as your server and 8888 as your port. Click OK to apply the settings.
After that, you can navigate back to the production server on which the problem exists knowing that your file will be inserted in place of the actual production file. The browser itself is none the wiser that the file has been swapped out, so you're safely able to debug readable code without making any changes to the code on the server. This technique has helped me debug some of the more complex issues I've dealt with at Yahoo!, and I hope that it can help you as well.