What caliber gun does Norma Desmond shoot Joe with? She shoots him in the back, he reacts and keeps moving. She shoots him again, he reacts and turns around. Then she shoots him in the front, he drops his bag, then tries to pick it up, stumbles and falls into the pool and dies.
Either he's really, really tough, or that gun didn't pack much power.

Given that he has three bullet holes in him, why don't we see blood in the pool?

When the police pull his body out of the pool, his coat doesn't seem to have any bullet holes in it.

you'd almost think he was an actor who hadn't really been shot...

Whilst you are right, KAM, there is probably no way they could show that kind of realism in a film without a much higher rating and therefore lower box office.

Sunset Boulevard was made in 1950, before the rating system existed. What existed then was the Hays code, a rigid and strictly enforced set of "Do", "Don't" and "Be Careful" rules that regulated what could and could not be shown in movies made in Hollywood. Realistic depictions of murder and firearms use were in the "Be Careful" category.