“Maybe the lock was bad?”
Who knows? Whether the door was open or not is relevant to the investigation as an open door would have made it easier for him to get in.
However a closed door was likely expected by the killer as he planned this slaughter. He had the firepower to get in so the outcome would not have changed.
Greater mistake IMO was the inept police response.
“He had the firepower to get in so the outcome would not have changed.”
Well, if he used an AR-15 to shoot his way through a door, that would certainly leave a mark.