Avoid becoming wanted at the mall
You can shoot a policeman one time at the mall and not become wanted by anyone. Shooting twice will knock the policeman down and turn into a wanted man. Note: Do not shoot the civilians.
In the hospital
When in the hospital, do not walk around with John or Sara Connor, which could get them killed. Instead, find Sara and leave John there. Sara will protect him while you are away. Then, complete all the other objectives and return to get Sara and John.