Sgt. Ames talks about the shotgun being ballistic tested. Standard Shotguns do not have rifling and do not fire bullets, they fire shot pellets. A shotgun does not leave marks that can identify it. Not by 1964 ballistic tests.
A male character picks up a female character in his arms with her face up. He then walks into the next room and immediately announces his intent to spank her proceeded immediately by the sounds of the action. It would take more time than elapsed to re-position the lady.
After the corpse falls into the swimming pool she moves her arms some to keep afloat.