Well about the possiblity of presidential aspirations of Arnold, I have a quote from Demolition Man:

Stallone: "Hold it! The Schwarzenegger Library?"
Bullock: "Yes, the Schwarzenegger Presidential Library. Wasn't he an actor?"
Stallone: "Stop! He was President?"
Bullock: "Yes. Even though he was not born in this country, his popularity at the time caused the 61st Amendment…"

Hrm... I have heard that Sen. Orrin Hatch has proposed a bill for an amendment to end the constitutional limit against non-native citizens.