Executive Meddling: Averted in the original. Tobe Hooper avoided excessive gore and showed the violence in quick cuts because he was originally aiming for a PG rating(!) The censors were pleased. The other films in the franchise are a different story altogether...
Leatherface: Texas Chainsaw Massacre III was completely destroyed by the censors and the executives.
Also, John Larroquette as the narrator in the original - one of his earliest roles. He reprised the role in the remake and its prequel.
Dennis Hopper stars in the second film.
Jossed: A lot of background stuff introduced in the novelization of the remake is rendered non-canon by The Beginning.
Money, Dear Boy: Michael Bay once stated the he only produced the remake due to the name appeal alone.
Troubled Production: The filming of the original was a miserable experience for all concerned; cast member Edwin Neal memorably stated that shooting some scenes were worse than anything he experienced while serving in the Vietnam War.