What happens if he gets shot? what happens if there is a serious accident? what if he is in his 40's and has a heart attack (happened to a friend of mine)? as for Heart attacks my dad had one over 25 years ago and after surgery and a bit of rest at the time he is still going strong. I don't see why age matters for the right person to be the leader.
As for early elections, I am neither an American or a political expert, but here in Canada (and many other democracies), there can be a vote of none confidence (or similar) and that triggers early elections but as far as I know there is nothing like that in the US. If, for any reason(health, impeachment, quitting....) the guy stops being President the VP becomes the new President and there is a clear line of successions. There can never be early or late elections they are always in Nov every 4 years. That is why in the US presidential elections are a tag team event and it is "I am running with X for vp) they could be stuck with that second guy as president for 4 years.