Here's the thing that gets me about this episode, Edward is doing the inventory by listing the pieces they have on a tape using a microphone. Why then, does Columbo not hear the first shot when he's listening to the tapes later?
He doesn't necessarily play the tape recorder continuosly; he stops and starts it frequently. Also, it's not a high-quality microphone that would pick up far-away sounds. It definitely could have made for a good extra clue though! One of those "there's something on that tape that bothers me..."
They also failed to note that the brother didn't have powder burns on his hand, which should have been there if he had fired the gun.