The first two days after I received my iPhone 5, I racked up 400MB of Cellular Data. 99% of the time I was using my phone, I was connected over WiFi. So I ran a test on my own by watching a YouTube video over WiFi and then looking at my Cellular Data under the Usage menu. Sure enough, it had went up by around 10MB. I called into Apple Support and asked them what was going on. They thought that it might have been a problem with my phone or my house's WiFi connection. After them walking me through a series of test and restores, the lady semi-acknowledged that it could be a problem with how their phone interacts with the new LTE network.
If you guys out there could keep an eye on your Cellular Usage Data, that would be great. Maybe it's a problem with my iPhone 5, or maybe it's a much larger problem. Seeing as I used to have unlimited data with Verizon, being charged with everything above 2GB would be very costly for me...especially when it's not even my fault.
Hopefully we can get this issue sorted out.
Here's how to enter the Cellular Usage menu: Settings->General->Usage->Cellular Usage