The victim was supposed to have been shot with a high-power rifle but nobody heard the shot. At the distance indicated a high powered rifle would make considerable noise not to mention the bullet would go supersonic and the crack of it passing the speed of sound would be audible to people in the vicinity even with music playing. (Though Hart does note that the radio might have drowned out the sound of the shot.)
When Barbara Michaels (Tina Romaine - the "surf broad") comes out of the surf and falls down, she is below the tide line - the sand where she falls is smooth. When the crowd surrounds her, she is above the tide line - the sand is rough with footprints and seaweed.
The murder victim was supposedly shot in the temple. Yet right before she falls to the sand there is no sign of blood or a wound on either side of her forehead.