I thought mine seemed better today, but then it had another episode this afternoon. I was watching a long Youtube video over 4G. About 5 minutes into the video, the whole screen started shaking. I stopped the video, and the display continued to shake. The entire home screen was fuzzy. The horizontal line for me appears at the top of the screen, so when it shakes, nearly the entire screen shakes. I rebooted, but the screen continued to shake.
Some people have also talked about a much more limited version of the flicker that seems to only happen on the App Store login screen. I'd be interested to know whether that is just a much more limited version of the issue the original poster and I are experiencing or if that is a different issue altogether.
It looks like my phone needs to go back. I need to find out what my options are. The Apple Rep kept giving me warranty repair options, but I am not really interested in having my phone repaired. I want a new one.