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.
Revealing mistake: During the castle scene, when Indy is swinging outside, the sky is clear and blue and obviously not rainy, yet it is still raining. And yes, sometimes it can rain when it's sunny, but take a look - it is NOT rainy weather.
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.
Revealing mistake: After the Nazi tank drives off of the cliff and hits the bottom, the upper turret breaks off. As the turret rolls over, you can see there is no hole in the bottom, just in the top.
Revealing mistake: When Indy is clinging to the side of the tank turret in the desert, to the right of the tank are tire tracks from the vehicle shooting the scene. They appear to just start at a set point. There was likely no way to hide this.
Suggested correction: There's no obvious moment in the film where tire tracks are visible while he's clinging to the side. A specific time or shot description is needed.
Other mistake: While Indy and Henry are aboard the zeppelin Indy tosses Vogel out the lounge window, and when Vogel shouts up to the departing airship, in the next exterior shot we see the zeppelin airborne against a scenic view. Later, when Indy realises the zeppelin is turning around it cuts to another exterior shot of the airship, and the scenic view is identical to the earlier shot, only it's been flipped. The images of the zeppelin facing two different directions were composited onto the same scenic background.
Factual error: When Indy and Marcus first arrive in Venice on the boat the dock they alight on to has tactile pavers (for the visually impaired) installed on the platform. These weren't invented until 1965, some 25+ years after the scene takes place.
Suggested correction: One piece of the pier looking different doesn't mean that is meant for blind people, could be just a repair, or decorative, or a coincidence, could be anything.
You can see it is a tactile paver as it has the raised spots.
Continuity mistake: The Zippo lighter on the floor, thrown by Dr. Jones, keeps moving around between shots.
Continuity mistake: In Berlin, Indy grabs his father's book from Elsa's trenchcoat. In the next shot, the Nazi pin on Elsa's tie has disappeared.
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.
Other mistake: Indy has been very careful to hide from everyone that Alexandretta is the city where the trail starts, only to give away all the essential info. He did not tell Elsa. Only Marcus (who has the rubbing of the crucial inscription) and Sallah knew. The only way that the Nazis find out is because he tells his dad, in a room which he KNOWS to be wired, i.e. bugged. (The Nazis also find the diary, but we know that the city isn't in there.) Stupidity doesn't quite cover it.
Revealing mistake: When Henry says "Faster, boy, faster!" to Indy when they are driving into the tunnel to escape the flaming aircraft, you can see the track that the flaming aircraft is sliding on.
Revealing mistake: When Indy shoots three Nazi soldiers with a single bullet during the tank chase sequence, you can see the blood packets inside their uniforms.
Audio problem: When Vogel is holding Elsa hostage in the castle, he points his gun at Elsa's neck and says "Enough, she dies." If you look at Indy's shadow on the wall, you can see Indy is mouthing the word "Wait." In the next shot, he is saying the word again, this time with audio intact.
Visible crew/equipment: After Indy's father is cured and the Nazis drop the weapons, he stands up and set lights are reflected on his glasses.
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.
