From Pearl's talk with Jed after he's struck it rich, it's clear that the Clampetts are ignorant of modern conveniences, yet Granny later makes reference to a telephone as though she has used one her entire life.
When the Clampetts are eating at the pool table, Tyler arrives and goes to kiss Ellie May's hand. She flips him over and it appears that Tyler knocks a pool cue over on his way to the ground that was propped up against a wall unit. In the next shot, it is back in its place, and no one was seen to have picked it up.
When "Jed was shooting at some food" and fired the shotgun, there was a noticeable delay of about a sec between the shot/puff of smoke and his jerking his shoulder back due to the recoil on the shotgun. If the gun had really been loaded and there'd really been that much recoil, his shoulder would have moved at the same time we saw the smoke/flash of the gun.