The Intellect
One of the most vital aspects of the character that they need to get right is the intelligence of the character, there's no use casting the likes of Vin Diesel, Dwayne Johnson or Arnold Schwarzenegger (as hilarious as that would be) you need to cast some one with a level of intellect about themselves, someone who knows exactly how to channel the aura of the character being of a higher plain of existence than those around him, the Doctor should always be the cleverest person in the room, and if he isn't then you're doing something wrong!