My pet seems to look out at the screen periodically and beat his paw against the ground. Does that mean anything?

Your pet is trying to interact with you. If you spend time with your pet, rewarding the actions that you like, you will discover all sorts of fun behaviors. I've seen my pets run across the yard and then slide, stand on their hind legs, and jump (to name a few fun things).

Thanks. I was guessing it was something like that. I do try to brush him periodically, but sometimes he moves when I'm doing that and I end up hitting him instead of brushing. I have seen him jump, and he keeps trying to stand on his hind legs.