I experienced a similar issue -- but on a much smaller scale. My clock was just stuck about 15-20 minutes earlier, and then updated after I toyed with it for a bit. I thought I'd share anyway, so my story is out there too. I've only noticed it once last week, although I have a feeling that it may have happened before... I just haven't really taken notice until the headline caught my eye. That's right guys -- this story is all over the media, so hopefully that will speed up Apple's fix! AppleInsider and CNET both have the story, as well as a few others.
I work and live in the same immediate area. I walk to and from work, and the walk is only 5 minutes. I live in Lincoln Park, which is a city bordering the southwest area of Detroit. Last week, I went home one day for lunch. I left shortly after 1pm. After getting home and eating, I checked my phone so that I wouldn't be late getting back. My phone said 1:05. Being that I had walked 5 minutes home, walked in the building, unlocked the door, prepared lunch eaten... I knew it wasn't right. I checked another source and it was around 1:15-1:20. So I started fiddling with settings. I remember toggling cellular data first, since the time is set from the network. Turning that off and back on didn't help. I tried turning automatic time on and off, and that didn't help either. I hadn't read any articles or this forum yet, so I didn't think to toggle LTE. At this point I don't remember exactly what fixed it... although I'm fairly certain it was turning the phone off and back on. I feel like after the reboot, it showed the incorrect time for 10-20 seconds and then updated.
I haven't had any problems with iMessage, push notifications or the like. No error messages saying that my date/time are incorrect. Most likely since the variance in my time wasn't nearly as much as others. It did happen in my home, like the others, and I'm also using an iPhone 5 on VZW. It seems weird that the time was stuck around the time that I left work... and the only possible explanation I can dream up is that when I passed through one of our dead zones by the time clock, that it didn't resync the time when it got back into service. It could very possibly be LTE related, because while I live in an LTE area, the heavy construction of my work building often causes our phones to fall into 3G or lose service altogether. Albeit, everyone else loses service more often while those of us with VZW tend to just lose LTE. (;
So there ya have it. Although the one Sprint user did post, it seems like 99% of the problems are with VZW. I'm turning off notifications to this thread because I don't want 30 million emails, and I probably won't think to come back to visit unless I notice the problem again. If anyone could benefit from further info from me, feel free to shoot me a message.
Lastly, I want to join everyone else in stating that Apple and VZW need to work collectively to get this fixed. Like YESTERDAY. They could at least acknowledge the problem so that we know a fix is in the works!