Maybe Henry the Third would get better if he's given an adventure to go to, a lady friend to take along, and the action of the first three movies.
In KotCS he was just this teenager running around with Indy, as if to make the audience surely realize that Indiana Jones is now an old man.
I think that if they'd put effort to it, they could make at least a watchable film with what they got. They'd just have to be careful with not making Mutt 100% clone of Indy. Similiar basics between the two are okay though. (While Indy has his beloved hat and the whip, Mutt has his beloved hair and the sword. Plus, he wasn't too happy when the scorpion bit him.)
And if Ford wants to quit being Indiana Jones, how about a scene between Indy and his son, in which Indy says that he's had enough of adventuring, or something? He could translate a piece of paper to Mutt or something, leave it to that and live happy ever after with Marion, never to be seen again.
And if he really wants to die he could be shown as a black 'n' white photograph on Mutt's table/wallet/etc. But I really wouldn't like to see Indiana Jones die on-screen.