I don't like Juliette's story arc. I guess they're using her to fulfill the oft-used Princess in the world of faerie tales?
I like Rosalee much better. Heck, Adalind's character is more interesting. Maybe if Juliette had a different actress, but I had her pegged for dead in the first season (liked her better then too, like when she dumped hot water on that guy).
But, there's two points about the police aspect you have to think about: Nick's superior has always known who he is and what he'd up to, so he's kept the Grimm part of his job tidy and away from the notice of the law.
And about the pilot episode song: She was a jogger, and some people set their runs to a certain beat to keep their pace. I JUST considered that flaw two days, which is pretty sad, but there's a reason I don't write mysteries.