My roommate and I have been playing a lot of Super Smash Brothers Brawl recently and we noticed that our inputs would drop frequently for random periods of time, ranging from so short you couldn't tell to around two seconds.
I mention Brawl specifically because one of its gameplay systems actually helped us determine what the issue was. For those who do not know Super Smash Brothers Brawl features a gameplay element called "tripping", in which every time you move the stick quickly in a direction to dash, there is a random chance that your character will trip, and fall flat on their face. We noticed that our characters were tripping more often than they should normally, and discovered that the connection between controllers was actually dropping for split seconds while we were dashing. The system interpreted this as moving the stick to the center position, and then very quickly back in the direction it was actually being held, resulting in multiple dash inputs instead of one, and a lot of tripping. Additionally, some attacks in the game require you to hold down a button to "charge" the attack, which would be unleashed when the button is released. We found that in almost every instance, the input was dropped and picked back up, causing these charged attacks to fire prematurely.
With that whole explanation out of the way, I'd like to share the solution we found. Our Wii U is sitting almost right next to our wireless internet router. Unfortunately, it is the best location in the house for the router, and it cannot be moved. Upon unplugging the wireless router, all of the problems ceased to persist, and upon plugging it back in, they all came back.
What's odd is that we've only noticed this kind of effect from the interference while in Wii mode, and while playing on an actual Wii. Wii U games appear to be unaffected. The video, audio, and input streams for the Gamepad work flawlessly. My assumption is that the Wii U uses a different type of wireless communication method with controllers than the Wii does, and that the Wii's method is utilized by the Wii U while in game mode.
Naturally, unplugging and plugging our internet back in is a bit a pain in the ****, and I'm looking into seeing if it's possible to just temporarily shut off wireless signal transmission on our router, which is better, but not perfect. Does anyone know of any wireless signal channels that don't interfere with communication between Wii controllers or something?