Keats was a pretty great character throughout season three. He was a bit of a creeper, and came off as very menacing. In the last episode they really spun him over the top to the point of being just downright silly. I didn't like that aspect. But I'll totally take the rest, even if the idea of a special purgatory for police officers is slightly sillier than the idea of purgatory in general. I think they left it vague enough that it worked. However, yes, Life on Mars and the test screen girl was pretty much perfect.

Just re watched Shaz's death, uniform is very modern looking, and the car shown is definitely newer than the 80's.

Maybe Chinese law enforcement officers who die in Hong Kong end up in some police department in Hong Kong in this purgatory world. Perhaps the powers that be in the LoM/AtA universe like to keep things culturally relevant to the tormented souls, but also like to screw with their heads by throwing them in a different time period. A cop from the 2000's thrown into a 1970's environment they have some familiarity with is going to be bewildered, frustrated, and confused. A cop from 2000''s Hong Kong thrown into 1980's England is going to be completely lost and have no idea what is going on.