Continuity mistake: When the tank is about to go over the cliff you can see that there is no one sticking out of it, but in the next shot, Vogel can be seen sticking out and yelling.
Continuity mistake: While the German tank travels to the temple, it passes a German soldier. Inmediately after, a very wide angle shows the soldier has dissapeared.
Continuity mistake: Jones Sr. falls on the tank's chain and passes by the turret and by a round rusty thing. When the angle changes, a second before Indy saves him with the whip, you see Sr. has moved half a meter back instead of forward, and is passing by the same elements as before.
Continuity mistake: When Marcus is taken to the temple by the Germans, the knot on his tie differs between a far shot and a close one.
Continuity mistake: When the Zeppeliner turns back towards Berlin, it is over snow covered mountains. But when the Joneses escape in the biplane there is no sign of snow anywhere.
Continuity mistake: Indy throws the German officer out of the zeppelin window and Senior stands up to watch it all better. Then he sits down. Angle changes to a wider view and Senior is back on his feet, head almost out of the window, repeating the previous movements.
Continuity mistake: Indy and a soldier fall down on the tank, right where some bags are. From the next angle they are half a meter before the place where the bags are.
Continuity mistake: When Indy is looking up at the front of the Grail temple it is bathed in direct sunlight. Indy dismounts his horse in the shadow. However, in the shot just before dismounting, the cliffs behind Indy are also bathed in direct sunlight. That is impossible.
Continuity mistake: When Young Indy is hoisted from the lion's carriage on the train, one of the baddies is holding a gun at him, in the next shot, the gun is down by his waist.
Continuity mistake: When Indy gives his father water from the grail to drink, the grail glows from inside, and the gold inside it is bright and even. But when Indy pours water over the wound, the grail is dark inside and there are dark patches in the gold. Obviously, they had to take the light that made the grail glow out so it wouldn't be seen when Indy pours the water over his father.
Continuity mistake: The 109s that are animated are shaped like the original German fuel injected ones. The shots where it's a real plane show the modified one with a RR Merlin engine that gives it a weird square nose.
Continuity mistake: The lion approaches Indy from the rear of the circus car and walks towards the center. Next shot, the lion approaches from the back of the car again.
Continuity mistake: The Joneses take off in the Zeppeliner from Berlin. Shortly after takeoff they are over tall snowy mountains but there are no tall snowy mountains that close to Berlin.
Continuity mistake: When Indiana pushes the Nazi colonel out of an open window, if you look carefully, the colonel fell a few metres out of the zeppelin before landing on a pile of suitcases, but when the colonel looks up, the zeppelin is several hundred metres above him, in too short a time to ascend that much.
Continuity mistake: When Indy enters the beach he steps on dry sand and then on the wet part. A frame later, in a wide angle, he is still stepping on dry sand.
Continuity mistake: Indy pours water from the grail into his father's mouth. Between two consecutive shots, the position of Indy's hand changes and the direction he pours changes 90 degrees.
Continuity mistake: The shape of the exploded canon barrel on the tank changes a lot in the different shots. Especially between the scene right after the explosion and the scene where Indy is hanging under the barrel.
Continuity mistake: The Zippo lighter on the floor, thrown by Dr. Jones, keeps moving around between shots.
Continuity mistake: When Indy shoots the three soldiers on the tank they fall sideways but not off the tank, a few seconds later all three bodies have disappeared.
Continuity mistake: When Sallah pulls his rifle and overtakes the Nazis at the Great Seal he is in the forefront with the Nazis in front of him and Indy and his father are behind him. Within the next scene he is now in the background with his rifle resting in his arms.
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.