Continuity mistake: Indy jumps on top of the tank from a slightly elevated path that's located next to the road where the tank is going. However, when Vogel emerges from the tank's interior, the camera focuses on the landscape behind the tank, and the path from where Indy jumped is gone. (01:31:25)
Continuity mistake: When Indy first shows up in the uniform inside the blimp, he turns to squarely face a man sitting in a chair near the wall. When it cuts to the next shot of the German, he's turned ninety degrees to the right. Too fast between shots.
Continuity mistake: During the fight on the Coronado's deck, Panama Hat is climbing the ladder with his back to the camera. In the next shot, when he says, 'Grab him, he's getting away!', he faces the camera. (00:13:21)
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)
Revealing mistake: When Indy kicks Kazim's partner out of the speedboat, the man grabbing Indy's body from behind is not Kevork Malikyan. (00:39:15)
Continuity mistake: After the Brotherhood of the Cruciform Sword members begin shooting, in the wide shot of the canyon gunfight (with Indy, Henry and Sallah in the right corner of the screen), Vogel is standing behind the tank, shooting at the Brotherhood with his Luger. In the next shot, he's suddenly running with two soldiers. (01:25:47)
Continuity mistake: At the beginning of the movie, in the shot after Roscoe says "He's got our thing!", the lamp behind him and the lamp in front of Fedora disappear. Also, just after Roscoe says that line, immediately his voice is heard saying "Get him!", but his lips don't move. (00:04:44)
Continuity mistake: The remaining Nazi biker passes among his fallen compatriots following Indy. The latter looks over his shoulder at the biker. In the next shot, the background behind the Nazi is totally different (the bodies, the motorbikes and the hut have disappeared). (01:04:53)
Continuity mistake: When Nicola Scott and her soldiers enter the room where Indy and Henry were tied, the window next to the fireplace is on fire. In the next shot, there's no fire there. (01:01:42)
Continuity mistake: The scene when the barrel falls on the TNT box and explodes is flipped (Panama Hat is on the opposite stairs). (00:13:44)
Continuity mistake: In the wide shot of the Nazi convoy, Colonel Vogel can be seen walking alongside a troop truck. In the next shot, he is no longer there. A few seconds later, the colonel appears from the right side of the screen. (01:23:49)
Continuity mistake: When the soldier walks up the steps to attempt the first trial with his sword drawn, in the shots from the front, he's holding the sword on his right side. In the shots from behind, he's holding it on his left side.
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.
Continuity mistake: When they first meet, Walter Donovan hands Indiana the glass of champagne almost filled to the brim. The next shot shows Indy's glass with much less champagne in it.
Continuity mistake: Indiana has his satchel on him at the beginning of the 3 challenges and up to the point when he is entering the resting place of the grail. As soon as he enters the cavern where the Knight is, and he stands up, he no longer has the satchel.
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.