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.
Revealing mistake: When fire sweeps through the catacombs under the church, you can see that the "rats" are completely fake. At the far left of the screen (widescreen) you can see several fake rats just hanging on the wall and not moving at all. In the "special features" section on the DVD, Steven Spielberg admitted that the rats were fake - he couldn't bring himself to roast live ones so he could not make this scene appear realistic.
Factual error: There are no catacombs in Venice! There are also no natural petroleum sources - but that seems secondary to the fact that the entire city is just below sea level - there are no sewers, no subways - nothing underground.
Factual error: In various scenes, Dr. Elsa Schneider (Alison Doody) is wearing the M43 (Mountain Cap). That cap was introduced in 1943.
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.
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: When the Nazi is strangling Indy with the chain, Indy looks down into the porthole of the tank and yells, "Dad!" Before he throws the gun down into the tank Indy's hat comes loose, but when the next shot is back on Indy, and he yells, "Dad! Dad, get out!" now his hat is back to normal.
Continuity mistake: After Sr. says "Let it go" as Indy is trying to get the grail, Indy is swinging and not being supported by the wall. The next camera angle shows him grasping the wall near his head. Switched back to Sr.'s view, he is again not holding the wall.
Continuity mistake: When Indiana is drinking champagne with the businessman in the fancy apartment he holds his glass by the stem in one shot and then by the bowl in the next shot. As the conversation continues the glass goes up and down in Indiana's hand like a yo-yo.
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: On the tank a soldier jumps from Indy's right to attack him. The following angle shows the soldier coming from the front.
Continuity mistake: When the Nazi Colonel discovers Henry Jones sen. aboard the zeppelin, Indy asks him for his flight ticket. In the first shot, Indy is standing right beside the colonel (the camera is behind the colonel and Indy comes in from the right), in the subsequent shot, Indy is standing behind the colonel.
Continuity mistake: While in the Germans tank, the right side of Marcus's jacket is bent and wrinkled. A Frame later it looks perfect.
Continuity mistake: Indy and co. leave their horses a way from the steps to the temple, but when we cut to a closer shot they're very close to the entrance.
Continuity mistake: In the Grail temple, when Salah says "Drop your guns please," he is holding a rifle. When Indy instructs his father a few seconds later to get up, Salah is not holding a rifle but has his hands crossed.
Continuity mistake: In the scene in the temple after the two soldiers attempt to get past the first task, the first soldier is seen on his back holding his head beside him. When Indy attempts the first task, both dead soldiers are on their stomachs with no heads in sight.
Continuity mistake: At the airport, someone is reading a newspaper. Instead of the year 1938, the date of the newspaper is 1918 (a guess: I think this mistake happened because the art director wrote the date in a rush, stretching the "3" in a way it seemed a "1" when the people of "atrezzo" saw it).
Continuity mistake: While Indy and his father are talking in the zeppelin, the amount of flowers in the vase keeps changing between shots.
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.