node/[nid]/edit does nothing. how to troubleshoot?
My first step would be to watch the request with Firefox's Live HTTP Headers.  This will tell you if the request is actually going out or not.

If it is, then you need to check server logs to see if the request is being processed.  You may also need to add some watchdog() calls in the core node.module to track it down.

If the request isn't going through, then I suspect you have some rogue Javascript that is intercepting the click.  Disable JS and retest.  Another possibility could be that you have a CSS positioned element over the tab, and that is actually catching the click event.  Go through the body with Inspect Element and double check all of that.