The use of music in this game is brilliant. I don't think I've ever seen it done better.
Jumping out of the plane to Power >>>
MTVN, the fact that you're pointing out something like not understanding how the police stars trigger, tells me you're approaching Saints Row the Third all wrong. A I don't give **** attitude is really needed to fully enjoy SR3. Don't think too much is my best advice

Just let the game engulf you with it's awesomeness.
And the best parts of the game are near the end; it just gets better and better, so stick with it. So many memorable moments in the last third of the game, it goes all the right kind of crazy.
The more I think about this game, the more I love tbh. Will be starting my second playthrough tomorrow.