What if you get pulled over in a rental car?

Moving violations are considered to stick to the driver of the car, and not the car itself. Anything you do while driving a rental car is still your responsibility.

Things like expired tags are, of course, the fault of the rental agency. The car probably has valid registration, but the branch hasn't gotten around to putting the new sticker on the license plate or the windshield yet (it happens).

You can explain to the police that the car is a rental, and there may or may not be a registration paper in the car's glovebox showing the rental agency as owner. Even if there is not, the fact that the car is a rental should be pretty obvious since most of them have a bar code sticker on a window, and such cars will be in good repair and unadorned.