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.
Continuity mistake: In the library scene Indy discovers the "X" high up on the balcony. The X is green with a grey background. When he breaks the tile to find the tomb the X has become a faint outline on the floor. (00:27:40 - 00:28:45)
Revealing mistake: In the catacombs of the library, Indy and Elsa are waist deep in petroleum. Indy has a torch, and if you look carefully, you will see burning pieces of the torch fall and hit the petroleum. Wouldn't this start a fire as Kazim later on sets the cavern alight with a single match? (00:34:05)
Plot hole: When Indy is stepping on the letters at the end, trying to spell out God's name, he steps on J, incorrectly, causing it to collapse. When he falls through, however, he grabs onto another letter so as not to fall down. The letters he grabs onto and pulls himself up are an L and a Y, which are not in the word Iehova, so should have collapsed too. (01:46:20)
Factual error: At the end of the classroom scene, Indy gives Marcus the Cross of Coronado. There is a pile of books on Indy's desk that he laters picks up and takes with him. One of the books (with the whitish spine, under the red book) is "Living Egypt", written by Paul Strand and James Aldridge. This book wasn't published until 1969, over 30 years after this movie takes place (1938). (00:15:20)
Visible crew/equipment: After Indy and Henry have escaped from Castle Brunwald, Indy jumps into one of the boats, pulls the motor starter cord and jumps back out, then just as he bends over to release the boat from the piling, right between Indy's legs the black covered arm of a hidden crewmember appears from under the tarp taking hold of the throttle, steering the boat away from the pier. (01:02:40)
Other mistake: At one point, Indy rolls off of the side of a tank, and somehow gets a strap around one of the guns pointing out from the sides. The end of the barrel has already been blown open by the rock he shoved in earlier. How did the strap get around that big cluster of metal, and then back again so he could climb back on the tank? (01:34:15 - 01:35:05)
Continuity mistake: When the tank goes over the cliff, the turret detaches upon impact. But in a subsequent shot, the tank is shown rolling over with the turret still attached. (01:36:35)
Continuity mistake: When Indy and gang are racing the Nazis to the canyon of the Crescent Moon, Indy looks at the Nazi convoy with binoculars. Close-ups of Indy show the sun is clearly behind him, and the binoculars are in his shadow. But then a glare from the lens alerts the Nazis to their presence. (01:24:25)
Audio problem: When Indy confronts the butler at the castle, we hear the butler say, "If you are a Scottish lord then I am Mickey Mouse." But his lips say something else. He actually said "then I am Jesse Owens." This line was changed because they thought that a lot of the audience wouldn't know who Jesse Owens (the black athlete who won at the Berlin Olympics) was. (00:46:00)
Continuity mistake: In the temple in the Canyon of the Crescent Moon, Indiana Jones rushes to his father's aid with the Holy Grail filled with water. He is shown pouring every last drop onto his father's wound by turning the Grail upside down, yet another camera angle shows his father clutching the grail to his chest, and there's still a bit of water in it.
Revealing mistake: During the "What happens at 11 o'clock?" joke, Jr. counts down ("12, 11, 10!" or something like that) with his hand, matte lines surround his hand to the point where it almost disappears.
Other mistake: When they go under the coffin you see the flame of the torch in the background. How could the flame go under the petroleum with them without either setting light to the petroleum or being extinguished itself? (00:35:55)