I saw the movie last weekend, and I've had some time to think about it and the scene that has stuck most in my mind is when Zod is taking off his armor and giving some speech to Superman. He ends up wearing a suit very similar to Kal's and then floats up about 5 feet off the ground. That was truly terrifying to me. Snyder grabbed a little bit of the Watchmen's Dr Manhattan for that scene, basically showing that these Kryptonians are immortal on this planet.
Spoiler:
I think Supes was forced to kill Zod because the General made it clear he would never stop killing as long as he was alive. And talk about vicious, Kal has no commitment to his fellow Kryptonians, he kills Zod, banishes the others to the Phantom Zone and defies his father by killing the embryos/ eggs stored on the Kryptonian ship