They can and do practice discretion all the time. I went to church with a police officer when I was a kid. He used to tell us there is the letter of the law, and there is the spirit of the law. Letter of the law states legally you should hand out tickets for doing 1mph over the speed limit, or jaywalking, or even littering in some places.
I had a buddy in college I was in the car with and he was pulled over and blew 0.01 over the legal limit. He was completely fine, coherent, and was actually pulled over for a bad brake light. The cop just let us call a friend to come pick us up and keep the car parked on the side of the road.
LEGALLY they may not be able to do certain things, but there is leeway.