Continuity mistake: Henry tells Indy "let it go" and Indy takes his left arm to where his father is. Half a second later his arm is away and he repeats the previous movement.
Continuity mistake: When Indy is in the cliff reaching for the grail, his hand swaps between clean, dusty and sweaty, between shots.
Continuity mistake: When the grail falls down the cliff and Elsa and Indy try to grab it, the ground it lies on is either yellow or brown. This changes back and forth and has nothing to do with lighting.
Continuity mistake: Henry pulls up Indy with both arms, but when the shot changes he is pulling him up with one arm only.
Visible crew/equipment: After Dr. Jones is healed, Indy tells him to stand up. Stage lights are reflected in Dr. Jones's glasses.
Continuity mistake: During the rhino scene, the roof of the carriage swaps from dark grey to blue before the rhino's horn goes through the roof.
Chosen answer: They're not, no. An individual doesn't become immortal after one drink - it requires them to drink regularly in order to remain alive. So neither Jones has been rendered immortal, merely healed of any wounds that they might have. But your surmise is basically correct - as the Grail cannot leave the shrine, any individual wishing to use it to prolong their life must stay there if they wish to enjoy its effects.
Tailkinker
Also, in Indiana Jones and the Kingdom of Crystal Skull, Henry Jones, Sr has passed away before the start of the story and therefore was not immortal.
raywest