To start off,

I know this is pretty picky, but it's kind of been bugging me.

Anytime someone isn't breathing, Jack starts giving chest compressions. Correct me if I'm wrong, but I just took a Red Cross CPR class, and when the victim isn't breathing, you only give rescue breaths. chest compressions have nothing to do with breathing; they are to pump blood through the body if the heart has stopped.

So why would a doctor try to pump blood through someone's body if he hasn't checked for a pulse and has no evidence that the heart has stopped?

I guess they wanted to make it more dramatic or something.