I have a similar problem but not the home button but the digitizer itself...
When out of the iPad everything works as it should but when I place the digitizer back in the case it acts as if someone was touching the screen in random places.
I have it down to the bottom left corner of the iPad mini. When I press that corner in it goes crazy but if I stick a pick or a piece of paper in that corner to elevate it it works fine. I don't think I can use it with a guitar pick sticking out of it...
any suggestions?