Continuity mistake: While Henry and Marcus are being held inside the tank, Indiana rides in circles and baits the tank to ram into one of the cars. In a following shot when we see Vogel walking toward the window inside the tank it's a flipped shot, note everything is backwards. Then two shots later, when Vogel shouts "quick" in German it's another flipped shot, and about five shots after that again flipped. (01:29:30)
Continuity mistake: When Elsa is looking out over the Canyon of the Crescent Moon, the sun is low - it is close to sunset. However when Indy is riding through the very narrow canyon, the sunlight reaches the bottom. It is not the same time of day (or later the same day).
Continuity mistake: When Senior is rescued from the tank with a whip around his ankle, the whip dissappears a split second later, when he is being mounted on the horse.
Continuity mistake: When Indy is rescuing his father from Brunwald castle, he uses his bullwhip to smash through the window of the room his father is kept in...but in the time it took to jump into the room and get smashed over the head by his father, the bullwhip he used would have lost lots of its momentum and it wouldn't be waiting for him to grab it and use it later on the movie. (00:47:40)
Continuity mistake: When they are first looking over the cliff at the tank, Sean Connery's beard is quite full, and in a shot moments later, still looking off the cliff, it has been trimmed.
Continuity mistake: During the big chase scene leading up to the three challenges, Indy uses his gun and begins to takes the high road on his horse. Harrison Ford couldn't seem to find the holster for his gun, so you can see his holding the gun by his side until the scene changes. (01:31:15)
Continuity mistake: The back of the boat gets chewed up by the prop in the same place twice.
Continuity mistake: After Indy exits through the sewer with his hair all wet, he escapes Kazim's men. When he turns around a block his hair is nicely combed and loose, instead of sticky. Not too plausible when you're running for your life and your head is soaked in petrol.
Continuity mistake: The distance between Indy's boat and the big red and white ship keeps increasing and decreasing randomly.
Continuity mistake: In the zeppelin, after Indy says "no ticket", everyone searches for their tickets and waves it at Indy. When the angle changes, a frame later, the people are searching for their tickets, no one is showing one.
Continuity mistake: The crater Indy's car falls into becomes bigger and way deeper between the first and second shot.
Continuity mistake: When the driver of the tank is shot and he changes the direction of where the tank is going, Indiana gets up, with his strap still stuck on the nozzle. However, in the next shot, he's become clear of being stuck. There's no way he could have gotten his strap undone so quickly.
Continuity mistake: Near the end, in the "Leap of Faith" scene, Jones steps off the edge of the abyss and discovers an ingeniously-camouflaged stone bridge. The camera pans to show the camouflage effect from another angle, and it's obvious that the stone bridge is only about one foot thick from one end to the other. Relieved, Jones scampers across to the other side, and the camera cuts again to show that the bridge is now a full three feet thick.
Continuity mistake: Before the propeller chops the boat, Elsa leaves and looks at Indy. Right then, the camera is reflected on her boat's windshield.
Continuity mistake: During the boat chase, after the one boat blows up, another comes up behind Jones and Elsa. Jones starts turning the boat. In the next shot, the man in the boat behind them is shooting at them. They're not turning, they're going straight.
Continuity mistake: Before they make the second fighter pilot crash, Henry hands his bag to Indy. In that shot, the handle of Henry's umbrella is closer to Indy's left shoulder. But, in the next shot from in front of Indy, the handle is closer to his right shoulder. Then, when Henry pulls the umbrella out, the handle is back near Indy's left shoulder.
Continuity mistake: In the cave, young Indy is giving instructions, his hair is down both sides of his face. When he removes the snake saying "It's only a snake", his hair style is changed.
Continuity mistake: The gap between Indy and the chasing motorbikes changes considerably between shots, close to him than far apart the close again and at the checkpoint out of sight.
Continuity mistake: The dirt road the solo motorbike rider takes heading towards Indy is completely different to the road Indy uses just after he knocks the solo rider off.
Continuity mistake: When Indy is on the boat and says "Too small for two of us!", it pans down and you can see the cross halfway out of Indy's pouch. Both of the arms and head are on the outside. Only the bottom half is in his pouch. The bad guy then proceeds to open the pouch, revealing only the top before taking it out.
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 ★