I think the seemingly indifference of Supes to the people around him is intentional - the dude is literally having the second or third fight of his life EVER, and it's over the fate of the world. Remember his dad virtually raised him as a pacifist - he didn't undergo any sort of military or martial arts training like Batman. He didn't even fight in High School! He's green as hell and he's learning to fight as a god for the sake of all humanity, so he did his best of taking the fight out of metropolis but his enemy is better and nastier. So he didn't have time to think about collateral damage. Maybe this is intentional and we'll see this issue addressed in the next movie.
In fact I still wonder how he can beat Zod since like Zod said, he was engineered to be a fighter. With equal strength and power (with Zod learning the new powers much faster than Kal-El), abd a much stronger motivation (Kal just betrayed and murdered his entire race), Zod should have murdered Kal-El instead, not the other way around. Unless he's a natural born fighter like Goku, (unlikely since his dad was more scientist than fighter), this fight should have been a very short and one-sided affair. But oh well, movies. In fact I kinda hoped that next movie we'll see Batman teaching a thing or two to Supes on how to fight bad guys.