Generally all states do not require emissions tests until the car is two years old and 99% of all cars are retired well before that time. Every now and then there will be a car that just ended up with low mileage rentals for it's entire life and an emissions test would be required for renewal but I think the decision is to always ditch the car regardless of mileage if that situation comes up.

In terms of an expired window sticker then more than likely the car is up-to-date with it's registration but someone forgot to add the actual sticker. Also, some people do steal them to put on their own car. People steal all kinds of things from the cars. I think that is generally why they will always remove navigation DVD's for cars that have factory nav.