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 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)
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.
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.
Continuity mistake: At one point Indiana's father blows the tail of the plane in which they were flying to pieces in an attempt to shoot at the Germans. This is obviously in a close-up studio shot. The next moment the plane is shown flying in the distance with its tail still intact. (01:17:45)
Continuity mistake: While Indy and Marcus are in the apartment in Venice, after Marcus says, "He knew everything, except the name of the city", he slams the diary shut. Then it's shown open, and he closes it a second time. When Indy takes it, it's once again open. (00:42:15)
Continuity mistake: When Indy is stepping on the letters, he steps on the "O" and knocks the "P" loose. In the next shot, the "P" is intact.
Continuity mistake: Inside the zeppelin when Indy and his father are talking at the table, notice the white handkerchief that moves all around the table. (01:13:50)
Continuity mistake: In the speedboat scene where Dr Schneider rescues Indy and Kazim from the boat that is chopped up by the propeller of a ship, she driving the speedboat with the steering wheel on the right-hand side. Seconds later as she drives the speedboat away, the steering wheel is on the left-hand side, obviously a flipped shot. When the speedboat slows down to allow Kazim to alight at the jetty, Indy is at the wheel which is now back on the right-hand side. (00:39:55)
Continuity mistake: When Indy is trying to hold Elsa and keep her from falling and she's trying to reach the Grail, you can see her hand coming out of her glove. In the first shot of her hand coming out, it comes almost all the way out. In the next two shots, her hand is about halfway out, then it slips out and she falls. (01:57:00)
Continuity mistake: In the beginning, when Indy is fighting aboard the Coronado ship, the very first time we see Indy in this scene (before we see him get punched), he is bleeding from the right side of his mouth. Throughout the remainder of the scene, he is bleeding from the left side of his mouth. (00:11:50)
Continuity mistake: When Sean Connery drops his lighter while trying to burn the ropes, the lid is flipped to the right. When he blows on it the lid then changes position slightly relative to the pattern on the rug, then when the rug catches fire the lid's suddenly flipped completely to the left. (00:56:40)
Continuity mistake: During the boat chase/fight in Venice, the rear of Indy's boat gets shot up and starts smoking and spouting flames and the engine starts chopping. He leaps onto the pursuing boat, fights until that boat is destroyed in the rotors, then leaps with the Grail protector back onto his original boat with Elsa. The boat is now running perfectly. (00:38:50 - 00:39:55)
Continuity mistake: In the motorcycle chase scene after the escape from Brunwald castle, Indy's hair is noticeably longer than it was in the castle scenes. It returns to the shorter length when they stop at the crossroads.
Continuity mistake: After Indiana and the Protector of the Grail escape the boat being chewed up, and the Protector reveals who he is to Indiana, watch his chest area... When Indiana asks "Who are you?" he is looking down at his chest (looking at the tattoo), and when we cut to Kazim you can tell he is holding his shirt open showing Indy the tattoo. Then when we cut to Indy and back to Kazim, his shirt is closed and he then opens it to show Indy the tattoo. (00:40:15)
Continuity mistake: In the beginning of the boat chase two bullets hit the windscreen of Indy's boat. In the next shot the location of the holes has changed.
Continuity mistake: When the zeppelin is shown turning around, the biplane that the Joneses are about to escape in is nowhere to be seen. (01:16:10)
Continuity mistake: When Indy takes the mail out of his pocket in the beginning of the film, he keeps the "Grail Diary" in his hand, but puts the letters down twice. Once before he opens the package and once after with the wrapper. (00:23:00)
Continuity mistake: As Indy swings through the window to rescue his father, he gets hit on the head by a vase. His hat is all crumpled and tipped quite far back, then in the very next shot his hat is neat and level.
Continuity mistake: WHen Indy is hanging off the side of the tank, his face becomes completely caked with dirt. After he gets back up on to the tank, his face is relatively clean. (01:34:40)