Continuity mistake: When the villains are following Indy through the caves, the old wooden bridge completely breaks and falls apart. However, when they make their escape across the same bridge, it's intact with only a couple of wooden slats broken.
Other mistake: In flashbacks, younger Indiana Jones has exactly the same voice as the older one.
Suggested correction: Harrison Ford's voice has always sounded the same. Watch any film he's done.
It's a noticeably "older" voice than in previous films when he was about the age his de-aged self is meant to be. I mean he's now in his 80s not 40s, of course his voice is different! An unavoidable mistake but still clearly different.
Harrison Ford's voice has definitely become pretty gravelly.
Continuity mistake: When Indy arrives in Tangier at Hotel Le Atlantique, it is evening. A party is going on in the hotel while the auction is being held. A discussion starts, and a fight breaks out. They go outside, and all of a sudden, it is daytime.
Other mistake: Dive boat interior, as the tablet is unboxed, there is a clear lens distortion as Indi looks round to his diver friend and the focus follows - giving a disturbing jolt to the image. (01:08:27)
Suggested correction: It just appears to be the result of the movie doing a slightly unconventional rack focus. I don't think that really qualifies as a mistake. If it does count, it opens far too big a can of worms in terms of various camera techniques being considered "mistakes."
Continuity mistake: While on the boat, Helena does her 7 spades card trick. When she gives Indy a turn, you can see the bottom card is a black 2. When she fans them out, it changes to black king of clubs. Then, in the next shot, it changes to 8 of clubs. (01:16:00 - 01:17:00)
Suggested correction: Not necessarily a mistake. She could be changing those cards by sleight of hand, while moving the 7 of spades into position for the final force. The mistake was not using the 3 of clubs for it.