I just can't find the "Use dynamic global hostname" option in Apple Air Port Utility 6.1 (610.31). Where can I find this option now?
Apple seem to have removed/hidden some of the more advanced options from the Airport Utility interface in version 6 and this is likely one of them. Unless there's a workaround someone else can suggest to make such options visible again, on 10.7 (Lion), I've been getting around this by using the AirPort Utility 5.6 for Mac OS X Lion. You can find the Dynamic Global Hostname option by clicking Manual Setup > AirPort > Base Station tab > Edit - though I'm sure you already know that :)
Note that I have the AirPort Express 802.11n (2nd Generation) and the Airport Utility 5.6 does complain that
when you try to configure it. It seems to read all the information correctly but I would urge you to export your configuration first and/or not have anything you can't put back after a full reset, if things go wrong.