Continuity mistake: When the tank goes over the cliff, the turret detaches upon impact. But in a subsequent shot, the tank is shown rolling over with the turret still attached. (01:36:35)
Continuity mistake: Inside the Grail's Temple, all the characters have the decapitated bodies of two Hatay soldiers and the two lion statues in front of them. However, when Indy's team is discovered and the shot changes, it can be seen from the position of the bodies and the statues in relation to the characters that they have all changed places, with the bodies now being to one side of the characters (to the left of Donovan and to the right of Indy). (01:41:55)
Continuity mistake: When we first see the knight guarding the Grail, his cloak is tied off with a braided rope, which hangs down on his right side. It stays this way until he says "You have chosen wisely," where the rope has somehow shifted to his left side. The rope goes back to normal when the knight waves goodbye at the end of the movie. (01:49:10 - 01:54:05)
Continuity mistake: In the temple in the Canyon of the Crescent Moon: After Harrison Ford cures Sean Connery by pouring water from the grail over him, Sean stands up with the grail in his hand. In the next shot, however, Alison Doody picks the grail up off the floor. (01:55:50)
Continuity mistake: When Indy is trying to hold Elsa and keep her from falling and she's trying to reach the Grail, you can see her hand coming out of her glove. In the first shot of her hand coming out, it comes almost all the way out. In the next two shots, her hand is about halfway out, then it slips out and she falls. (01:57:00)
Continuity mistake: When Indy is stepping on the stones with letters, he steps on the "O" and knocks the "P" loose, then it cracks and collapses. In the next shots, the "P" is perfectly intact.
Continuity mistake: When Indy comes face-to-face with Hitler he hands over Henry's diary with its black elastic around the back cover, but in the closeup as the signature is being signed the elastic is around the front cover, then it's around the back cover again when Indy takes the diary back.
Continuity mistake: When Indy and Vogel are fighting atop the tank we see the soles of Vogel's boots and there is a red hexagon dot under each heel, but while Indy is hanging off the tank's side mount gun the soles of Vogel's boots are different.
Continuity mistake: In the temple in the Canyon of the Crescent Moon, Indiana Jones rushes to his father's aid with the Holy Grail filled with water. He is shown pouring every last drop onto his father's wound by turning the Grail upside down, yet another camera angle shows his father clutching the grail to his chest, and there's still a bit of water in it.
Continuity mistake: In the motorcycle chase scene after the escape from Brunwald castle, Indy's hair is noticeably longer than it was in the castle scenes. It returns to the shorter length when they stop at the crossroads.
Continuity mistake: In the beginning of the boat chase two bullets hit the windscreen of Indy's boat. In the next shot the location of the holes has changed.
Continuity mistake: As Indy swings through the window to rescue his father, he gets hit on the head by a vase. His hat is all crumpled and tipped quite far back, then in the very next shot his hat is neat and level.
Continuity mistake: In the boat chase, when the bad guys are using machine guns, in one shot we see Indy's boat in the middle of the canal. In the next shot (close-up) they are very close to a large pile of dirt (or wood chips) and in the next (wide) shot they are in the middle of the canal again.
Continuity mistake: When Indiana is showing Marcus the Grail Diary in his fathers home, he closes the book 4 times in a row without opening it - first 3 times inside the room, and then once on exit.
Continuity mistake: When Indy and Elsa escape underwater, and surface from the tunnel, Indy's suit should be drenched, but it only has water stains. Then during the speedboat chase, their clothes are completely dry.
Continuity mistake: Indy falls off the side of the tank and gets his shoulder strap caught on the gun - this should not be possible because his shoulder strap is underneath his jacket, as can be seen when he gets back up onto the tank.
Continuity mistake: At the very end there is a large near circular blood stain on the left sleeve of Sean Connery's shirt. When they ride off, the stain has disappeared completely.
Continuity mistake: When the military caravan with Brody is driving through the canyon towards the Joneses and Sallah, the sun is behind Brody (discernable by the shade). But when Indy is looking down on them - from the front - the sun is also behind him.
Continuity mistake: The sky colour/condition changes between the shots of Indy and his father in line to get on board the Zeppelin and the scene just before. In one, it is cloudy, and in the other it is a clear blue.
Continuity mistake: When Old Dr. Jones is holding Young Dr. Jones while he is reaching for the grail, watch Indy's left hand. In the shot from above, it is by his side, in the shot from below, he is holding the rock. It keeps switching from his side to the rock.
Answer: Henry says, in response to Indy asking if he remembered the details of the trials: "I wrote them down in my diary so that I wouldn't have to remember." So, obviously he did NOT know them by heart. Also, as the other answer says, they didn't want the diary to either be in the Nazis' possession or be burned.