I've had this documented in my personal notes for awhile, but it dawned on me today that perhaps others out there may benefit from my experience, so I am going to post this publicly.
Last year Google provided attendees of Google I/O a very nice tablet -- the Samsung Galaxy Tab 10.1, not to be confused with the retail version of the 10.1, this edition has the "army of androids" on the back, and has a slightly different version of Android on it. Unfortunately, it also seems to have a habit of occasionally getting stuck into an "infinite reboot" state. The tablet will freeze, restart, run through the initial startup animation, pause, and then restart again. Repeat ad nauseam until the battery dies. I've had my tablet get into this state twice since I got it. Rumor has it, if you report the problem to Samsung, it is a ship-back-to-the-manufacturer type of problem, but if you have a few technical skills, this may not be necessary.