Hello,
I have this exact same problem, but no solution yet. My Ipad 3 is 1.5 years old, and during that time, it has worked flawlessly. Suddenly one day, I picked up my ipad to see that my screen was scrambled. After fiddling with it for a while, I realized that I could descramble the screen by detaching or reattaching the magnetic cover. I took it to the apple store to see if they could fix it but they had no ideas. They said that they had never seen this happen before. We decided to try erasing the unit and reinstalling the OS. That did not help. Now after about 4 weeks of temporarily correcting the problem by attaching or detaching the screen, just like you, my problem has gotten progressively worse, and now I can't restore it no matter what. Tried using some different magnets, but that didn't work. I figure there must be some loose metallic dust inside the unit that is repositioned randomly by the cover. Sorry no help, but thought you'd like to know there is someone else out there with the same problem. Will post a solution here if I determine a fix.