The only thing to peel off on Invisgrip is the paper backing. I'm sure you did that. Invisigrip is not fool proof by any means. I like it better than any other method I've tried but it is not perfect. You have to really learn to keep you hand near where you are cutting. With long rulers you have to walk your hand as you cut.
I'm no fan of the dots either. They raise the ruler up oddly and make things difficult for me. I have them on some rulers and do use them, but I don't love them.