Continuity mistake: During the temple quake sequence towards the end of the film, Elsa fails to maintain her grip on the rising earth and falls onto tilted ground, sliding towards the chasm. At this point, Sallah is kneeling on the ground, but in the very next shot, he is now grabbing hold of Henry.
Continuity mistake: When the Hatay soldier is decapitated in an attempt to navigate the temple's defences, his head rolls along the ground and Elsa turns her head around and looks over her shoulder. In the next shot, she has now turned her full body around, and in the shot after that, she is looking over her shoulder again.
Continuity mistake: When Elsa's hand slips from its glove whilst Indy is holding on to her, Elsa falls and she is holding the glove in her right hand, but when she falls into the chasm, the glove has gone.
Revealing mistake: When Sallah rides up to the tank to help, just as Indy shouts, "Get Dad!" in the closeup and wideshot of Henry we can see that he's actually lying on protective support, and not lying directly on the moving tank treads. (01:35:40)
Visible crew/equipment: When Indy tries to reach the Grail his father convinces him to "Let it go" and Henry pulls his son to safety, then in the next wideshot of Indy, Henry, Sallah, and Marcus a crewmember wearing a short sleeved, white shirt and blue pants can be seen at the right side of the screen, just before it cuts to Henry's closeup. This crewmember can be seen again after the closeup of the knight. (01:57:45)
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)
Visible crew/equipment: After Young Indy locks the two treasure hunters in the reptile train car he pulls a snake out of his shirt, and just as the third young treasure hunter tackles Indy we can see a crewmember's arm and equipment at the left side of the screen, before it cuts to the long shot. (00:07:00)
Revealing mistake: The stuntman who saves Indy's dad from the tank has a perfectly trimmed beard and a thinner face than Sallah's.
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).
Revealing mistake: When Indy and Kazim are fighting on the front of the boat, the front of the boat doesn't move at all when the huge propeller hits the rear of the boat.
Revealing mistake: The candles that adorn the wall in the Grail room do not appear to have a strong enough flame to put out the light they do that shines on the wall. In fact, it looks like there are electrical lamps just behind the candle. (01:49:20)
Factual error: When Indy and Marcus fly to Venice, the route map shows them going from New York to Botwood, Newfoundland, then from Botwood to the Azores to the continent. There were two transcontinental air routes at the time across the North Atlantic: one from New Work to Botwood to London, and one from New York to the Azores to the continent, but none from Botwood to the Azores. (http://people.hofstra.edu/geotrans/eng/ch3en/conc3en/earlyairnetworks.html).
Revealing mistake: When Elsa falls through the crack in the hole, she is swallowed by a big cloud of smoke in the void. However, her silhouette is visible underneath the smoke, revealing she never falls any deeper, and thus giving away how shallow the hole was.
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)
Visible crew/equipment: By the cliff, Indy's hat comes rolling towards him. Watch closely and you'll see a long shadow a meter above the ground, parallel to that of the crew member throwing the hat.
Other mistake: In the scene with the tanks, Indy rides up beside one with a rock. Watch the gun closely. The end of the one that he is supposed to shove the rock into is wobbling inconsistantly with the rest of the gun, or the tank for that matter.
Revealing mistake: When the VW gets stuck on the front of the tank and is shot off, you can see that the car has no engine, no body in the car, and no clutch. Also, when the car is blown away you can see a wire used for the stunt fall right in front of the camera.
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.