The filmmakers discovered to their chagrin that the snakes used for the Well of Souls sequence weren't afraid of fire at all - in fact, they would always try to get closer to the fire to warm themselves. At one point director Spielberg was caught on camera picking up a snake and telling it, face to face, "In the script, you're supposed to hate fire. Why do you like fire? You're ruining my movie."
When Belloq is yelling at Indy on the island from down in the canyon, you can see a fly crawling about his face. He doesn't flinch, nor does he make any attempt to shoo it. It eventually ends up in his mouth, and he still doesn't react. In editing they removed the few frames where the fly flew off, in order to give the impression Belloq ate it (http://www.theindyexperience.com/interviews/paul_freeman_interview.php).
Actor Michael Sheard appeared uncredited as the UBoat captain in Raiders. He also appeared uncredited as Adolf Hitler in the Last Crusade.
The canyon where Indiana confronts Belloq and the Germans and threatens to blow up the Ark is the exact same canyon where the Jawas take R2-D2 in "Star Wars".
The scene where Indy shoots the sword wielding bad guy wasn't in the original script. Three months' shooting had resulted in Harrison Ford having a nasty case of dysentery, and the choreographed fight would have taken three and a half days to shoot. Harrison Ford really didn't want to stay on set that long, so suggested that it would be a good alternative if he just shot him. Who actually suggested the change isn't certain, but it wasn't a spur of the moment decision, contrary to some thoughts - it was a planned alternative.
When the Nazis have taken the ark from the Bantu Wind (Captain Katanga's ship) and no one can find Indy (until he climbs aboard the sub), Spielberg actually filmed Indy diving off the ship and swimming all the way to the sub. Harrison Ford did the stunt himself, though the footage was never used.
During filming of the fight scene around the German flying wing, Harrison Ford slipped and fell down and the plane's wheels rolled over his left knee, tearing his ACL. Rather than trust in the local medical care, they simply wrapped the knee up tightly, applied ice, and kept on going.
When Indy swims to catch the U-Boat, the DVD and video cut out the part which ran in Canadian theatres (if not wider) where he lashes the whip to the periscope. This is probably due to the fact that just previously, Indy used the whip while he was dragged at the back of the Nazi truck and never picked it up. It was loosely hanging and about to fall away from the truck. I am assuming this was pointed out to the producers and they cut out blatant evidence of the whip being used.