I thought it was never really explained that Khan was previously a tyrannical dictator from Earth's past. Maybe I missed it, I've only seen it once, but I got the impression that one would only know that if they remembered it from the show.
There was some kind of 4th wall breach going on there with the Khan reveal. John Harrison says "My name is... Khan!" and there is this dramatic pause with concerned looks. Like Kirk and Spock knew who he was because they already watched Space Seed and TWOK.
Later on, nuSpock contacts original Spock and asks him if he knew Khan. How did he get that idea? Khan was adrift in space, why did nuSpock assume that original Spock met him? Because he subconsciously knew what happened in Space Seed again?