I think the worst part about TNG is that they never revisited some of the former planets TOS went to, precisely to see what happened to them and perhaps show a different pov on the necessity of the actions taken by TOS. Piece of the Action, etc would have been most interesting.
They also dropped the Preservers/parallel development angle entirely, which could have been good. And instead of aliens using the Paramount period wardrobe (Romans, Nazis, etc) they went to the forehead widget. Ah well.
"Piece of the Action" was almost a pure comedy. I don't think the more stiff style of TNG would have done a sequel to that episode very well. Either the comedy wouldn't work or they'd play it straight, which would kind of defeat the purpose.