If you try another red dot and see distortion in the dot, try taking a picture of it. If the dot looks like it oughta in the pic, the problem is your eyes. That doesn't address the battery cover of course. Sounds like a lemon in that department.
I have a Fastfire. To my eyes, the dot is distorted as you describe. I use it anyway. The trick is to not use it like you would an iron sight or bead. With metallic sights you focus hard on the front sight or bead and let the rear sight and target blur out. With a red dot you just look at the target and let the dot ghost over it where you want to hit.
Holographic sights work better if your eyes don't like red dots. Supposedly Trijicon red dots are a little better.