As to Scotty's actions, yeah trauma does make people do strange things. The scene in Saving Private Ryan where a soldier pauses to retrieve his severed arm is a case in point, and based on actual events. Major Reno at the Little Big Horn wandered off for a good hour or so to find the body of his friend while he and his men were trying to prepare for the Indian attack.
With regard to not noticing a missing planet, if they knew Ceti Alpha VI was their destination, and they plotted a course to there, apparently finding it where it should be, would they really have been counting planets? It someone charted a course to a specific Caribbean Island, and had never been there before, would they notice if another island just happened to have gone missing?