Isn't this a plot hole? (Spoilers)

Why did people in the movie think Dave was the killer?

People knew from the local TV news that Katie was killed by a gun and hockey stick. The police, Jimmy, and Dave's wife, and Dave himself, all of them should knew this. And they also know that Dave doesn't have a gun or a hockey stick. How come that didn't cross their mind? And Dave, he was smart enough to point out that the blood in the trunk of the car could have nothing to do with him since it had been stolen, but dumb enough not to prove to his wife or to Jimmy that he had no gun or hockey stick to commit the crime? Isn't that an obvious thing for him to do?