Yes, it is a known problem, although thankfully it's not too common.
I'm sure you all are trying to help when you say "it is definitely an app" or "it's because of the ATK," and obviously this isn't happening on your phones, which is lucky for you. You also have not seen all of the DX threads on this issue. For those of us that received a defective device that reboots constantly, the real fix is to return it for a new one (advice directly from Motorola Support Forum manager). I'm not saying not to troubleshoot it, but please believe that there are defective devices out there.
I tried everything before ordering a replacement (and yes, they sent a brand new one...actually my third brand new one (first had screen issues)). My DX actually rebooted by itself while sitting on the activation screen after a factory reset! Tell me what app caused that. It rebooted in Safe Mode, after factory resets, with no third party apps loaded, while sitting still, while on the phone, in and out of Airplane Mode, on wifi, not on wifi, in my pocket, and during the screen timeouts.
Bottom line - there is a known issue that affects a small percentage. It's not his imagination or caused by an app or ATK or The Weather Channel app. See the Motorola Forum and the 400+ replies and almost 30,000 views on the topic. There are also rumors from Motorola that it will be fixed in 2.2. I ordered a replacement rather than waiting.
There are other known issues not caused by apps or user error such as flickering screens, banded screens, yellow-tinted screens, soft spots in screens, dead pixels, and GPS radio issues.
Go get a replacement if you get a bad phone...you paid for it.