I haven't gotten my nexus yet, but I have a S3 and that thing reboots for no reason sometimes.
There's something wrong with it. I and my wife both have S3's on different carriers and have never had random reboots for the year we've had them.
The Nexus7 2013 random reboot issue is very real though. When I had mine, it would reboot (I caught it a few times doing the nexus X logo) w/o even using it. Same software as the old Nexus7 2012 so it wasn't a software issue.
Mine would also randomly drain the battery to zero and would need to be charged for a while before powering back up. The N7 2012 lasted longer w/ similar charge start times.
So two very real problems that bugged me enough to return it. I didn't hit the GPS issue because I didn't take it out of the house and didn't see the multitouch issue, but I'm always holding it, not using it one handed on a table...