Chux, you are right about the NES video quality. I played Punch Out in both Wii mode and Wii U mode and it looks 100x better on the Wii. Unfortunately, I hate the way NES stuff maps to the classic controller, and you can only remap in the Wii U version. I'll probably refrain from buying any more NES games until this is fixed.
Still couldn't beat Soda Popinski in either version, on TV or gamepad. I'm actually really good at this game! As a test I just loaded it on an emulator and beat Popinksi's ass with keyboard controls. I then played some Street Fighter 2, and didn't have any issues whatsoever, so I imagine that the issue is that there is the tiniest bit of lag in the system (either in display or controller, I can't tell) but it's so minute that only Punch Out seems to be affected.

