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)
Suggested correction: You still can see one "leg" of the X on the floor, it's only darker than viewed from above because the camera angle and illumination set used.
I think it is meant to be an optical illusion.
The "X" is first shown as a dark green "X" on a beige background. Next, we are shown the same dark green "X" that is barely visible over a green background. I think we are meant to understand that the beige square tiles were lifted away in a cut scene.
I see no reason why they would replace the floor just for the higher shot, it's the same floor throughout the scene. When they enter it's the same floor we see later as they are going into the hole. It's probably not a real marble floor, so they can use a styrofoam or plywood tile that Harrison can lift, one that matches the surrounding tiles. They don't shine as much as the rest of the floor. In the shot up high there is different lighting, so that could explain it. It just appears to be different. Of course, sudden different light can be seen as a revealing mistake.
Suggested correction: Not a mistake, just a different viewing angle.
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)
Suggested correction: It is not clear that the glare is coming from the binoculars rather than the car behind them (after all, the Nazis target the car with the tank).
They see a glare rather than a car. But anyway, regardless, the problem remains that the sun is behind the car too.
Factual error: Jehovah is spelled Iehovah in Latin. However medieval languages (Latin or vernacular) had neither official rules nor the letter 'J'. It was not until the sixteenth century that the French humanist Pierre de la Ramée proposed to use the 'J' as a separate letter distinct from the 'I'. The 'J' could therefore not have been a trap at the time the test was constructed. (01:46:20)
Suggested correction: The concept of what looks like a "J" was sometimes used when writing numbers in Roman numerals, originating sometime in the Middle Ages. While "J" did not exist as a letter at that time, what visually looked like a "J" did exist at the time the Trial was made. The purpose is to weed out those who can't spell the word of God...there's nothing implying that whoever created it meant for all the tiles to be understood as just letters.
Revealing mistake: When Indy is breaking through the wall in the catacombs, and he uses his shoulder as a battering ram. You can see his head actually bounce off a piece of the rock real hard as he is going through the wall. If the rock was real, I guess Indy would have a lot to cry about that night. (00:32:00)
Suggested correction: This rock is real but very old. That's why it was easy to break.
Trivia: While in the Zepplin Jones Sr. comments on not having his glasses on. If you look carefully the paper is upside down.
Suggested correction: Henry Jones Sr. does not mention his glasses whatsoever in the scene. The newspaper is upside down, but likely because he wasn't paying attention to it. He was using it to hide.
Other mistake: On the zeppelin, Indy's dad says, "You left just when you were becoming interesting..." Harrison Ford is mouthing Sean Connery's lines. (01:14:50)
Trivia: John Williams, the composer, used pieces of his score from Star Wars in this film. For example when young Indiana is on the roof of the train, you can hear bits of Star Wars.
Suggested correction: Is there an interview of John Williams saying this? Because this sounds like opinion. I personally don't hear it. There is a wonderful behind the scenes documentary on the DVD that goes in depth into the scoring of this movie. Neither John Williams, nor Steven Spielberg, nor George Lucas mention this.
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: When Indy is pouring the water from the Grail onto his father's wound, we see him pour all the water out. When his father takes the Grail, there's now water left inside.
Suggested correction: Automatic refilling seems to be the least of the miracles the Grail has performed.
There was no evidence of this, plus we never see it refill before or after. How would it be empty when they first find it if it miraculously refilled itself? This is a poor correction just to make a correction.
Factual error: When Indy and his father rotate into the control room, the eagle on the uniform of the woman who raises the alarm is on the wrong side, left instead of right.
Suggested correction: As it's an SS uniform, the eagle insignia should be on the upper left arm.