Things that didnt make sense on the original Star trek.

The crew that was selected to go down and investigate planets.
I can understand why Kirk would bring Spock and McCoy, A science
officer and chief surgeon would come in pretty handy. But If I was
captain, under no circumstances would I bring my best engineer(mechanic)
or best helmsman. They belong on the ship at all times.

I have to agree with you on that. I never thought about that much until I saw The Next Generation, when the 1st officer Riker refused to let Picard the Captain go on an away mission. That seemed more like the way it should be. I mean the Navy would never let the Captain of a ship be put at risk in that way.