We have the wireless guitar that came with Guitar Hero 3. There is an issue when playing RED and YELLOW notes together. When R and Y are pressed, strums trigger GREEN, so you cannot play RED YELLOW notes. But, I did find that if you strum up, it works.
I have tried taking the neck off and cleaning the contacts with a pencil eraser. That did not help. I also tried compressing the neck to see if better contact would fix it - it did not.
I've found multiple threads online where others discuss the problems they are having with this guitar. I've found others having the same problem I am.
One person supposedly figured out a fix but their English is not great. Have a look here:
Here is another thread where people discuss problems and possible fixes: