My puppy was a sneak peer and pooper. It was not just puppy mischief, it definitely had to do with dominance and marking. The sneaky part had to do with him being yelled at/struck by an ******* former owner (we found him at the pound).
I know the peeing has to do with dominance because husband coddles the dog and allows him to sit in his lap, etc., which the dog repays by peeing on his side of the bed. The dog will also sneak upstairs and crap in the unoccupied rooms (meaning, "hey, you aren't using them, so they're mine now").
Our solution is to crate the dog when we aren't in the house. The crate is a wonderful tool for training a dog. Dogs learn to love them, believe it or not. When the dog is not in his crate or outside, he is supposed to be on his "spot" (his beanbag bed.) Unless I am playing with him, feeding him or petting him, he is on his "spot".
Besides the crate and obedience training, try pleny of exercise. That should cut way down on negative behaviors.