iPhone 5 Touchscreen Problems

Just unboxed the iPhone 5 and for the most part it's great. But one big problem has been occurring with the touchscreen, which I've heard is new (integrated with the display itself versus a separate capacitive layer as in past iPhones). I'm curious if anyone else has been having this issue or has any suggestions on what to do...

The touchscreen acts up by "sensing" my finger even when it's not actually touching the screen, but is just very close. This happens gradually at first, then it seems to get a little worse, requiring me to use more exaggerated gestures to actually get the phone to do what I want it to do. Eventually the phone will just respond to my hand waving above it even several millimeters above the screen, and seems to go haywire. It starts missing the letter/button that I'm trying to type. Sometimes the whole screen freezes to where I can't swipe to unlock, slide between home screen pages, etc. Although the physical buttons like the home button and standby button do seem to still respond despite the touchscreen being messed up or frozen, it doesn't get rid of the problem when I go back to what I was doing.

Eventually, I end up resetting the phone by holding down both the standby and home buttons simultaneously for a few seconds. When the device powers on again, it seems to have done the trick and the touchscreen is back to normal. However, the problem reoccurs with a fairly high/annoying level of frequency. (I mean I've only had the device for a few hours total and it's already happened at least half a dozen times.)

Has anyone else experienced this? Does this sound like I have a lemon or could this be a general issue? I wonder if it can be fixed with a software patch or if I need a replacement screen/device. Pretty frustrating to deal with right out of the box, and I don't really want to go anywhere near an Apple Store today with all the craziness that's probably taking place...