I have followid information found on another forum and have managed to successfully install the update. It appears the issue is tied to the Ethernet connection. Strange, usually the problems I have with my Apple TV3 are related to using Wi-Fi rather than connecting via the Ethernet Cable.
At this point I have tried the following:
Reboot the device as suggested by the on screen information. (no resolution)
Clear the cache and reboot. (no resolution)
Unplug the AppleTV power cable and let sit three minutes before repowering. (no resolution)
Unplug the Ethernet Cable and connect to the Internet via Wi-Fi. (solves the problem)
Apple needs to test these updates a little further and make sure they work on all methods of connecting. The issue should have been remedied quickly by either fixing the patch or at minimum sending us an E-Mail notifying us of the error. In fact, why am I not getting an E-Mail letting me know that a new version of software is out? Isn't that one of the things we opt-in for when signing up for accounts?
For a direct link to the help document I followed use: http://www.macobserver.com/tmo/article/how-to-fix-the-apple-tv-5.1.1-ethernet-up date-bug