I've dusted my system and vacuumed it out and it's still running into it.
I'm trying this fix from NeoGaf out to see if it helps any.
TanookiTom found out about it via his XboxOne.
Sorry for bumping this old thread. I was having these exact issues - extreme stutter on the Gamepad including the sound - for the past two days.
I did some googling and found out this was because my Xbox One was in the "Standby connected" mode, downloading a game in the background. When the Xbox One is completely shut off there is no problem.
This together with the Fact that the Xbone still uses 15 Watts while in this fast-turn on mode, made me switch that off very fast.
http://www.neogaf.com/forum/showthread.php?t=1041520
Hoping that turning off the similar settings via the Wii U will help.
Went to the Power Settings area and then clicked on that and disabled the Auto Power-Down and the Standby Functions.
Here's to hoping it works out!