I had this as well, and mine was from a new phone (ordered online on launch day). It started doing this about 1.5 weeks after I got it. It is very intermittent, like around 1-2 weeks in between occurences sometimes, and there seems to be no clear cause for it.
I had other issues as well, like redrawing when going back to the homescreen, intermittent force closes, and the worst was having to frequently refresh Google.com page to do a search otherwise when I typed in a topic and hit search nothing happened.
It came to a head last night when my Rezound wouldn't connect to my Network Extender. When I dialed #48 it said I was under Network Extender coverage, but my signal was -105dBm (same as without the NE). So I tried restarting, no difference. Then I did a battery pull & it started random rebooting. It would let me have access to the phone for about 30 sec's to 1 minute after the homescreen appeared but before it rebooted again. It got to around 10 reboots before I got someone from VZW tech support from my land mine. We did a master reset and it still wasn't showing any better signal so they decided to send me a new one.
About an hour after I got off the phone with them the signal came back. I've got the phone mostly back to it's previous setup except for personalized ringtones & music playlists, but all apps are loaded up again. So far I haven't had it occur, but since it's only one day since the reset it's very possible it's not fixed and I just haven't seen it yet. When it first happened I assumed it was a hardware issue rather than software, like maybe a run of phones had a bad solder joint causing it.
What worries me is the phone Verizon's sending me is an unknown entity. I may have other issues with that phone that I don't have with my current one. The only reason I agreed to then sending out a replacement is because at the time I had no way to make calls with it, so there really wasn't a choice. I'm kinda hoping that I see the double screen issue before the replacement arrives so I'd feel better about returning my current one.
The only thing I can think of would be the fastboot feature, but I didn't enable that until about a month after the double screen issue first appeared, so I don't know.