In the opening sequence, Indy is a Life Scout. Harrison Ford was a Boy Scout in his youth, and attained the level of Life Scout.
Indy tells his class "If it's truth you're interested in, Dr. Tyree's philosophy class is right down the hall." When he was in college, Harrison Ford took a philosophy course taught by Dr. William Tyree.
Casting Gag: Sean Connery was cast because Steven Spielberg and George Lucas thought the only man who could play Indy's father was James Bond, and because the whole franchise was born out of Spielberg's desire to direct a James Bond movie — so in every sense of the word, James Bond is the father of Indiana Jones.
Not a gag, but Julian Glover (Donovan) and Michael Sheard (Hitler) were both in The Empire Strikes Back (also Lucasfilm, of course). Glover was General Veers, commander of the ground forces assigned to Vader's Super Star Destroyer Executor, who led the assault on Hoth. Sheard played Admiral "You Have Failed Me For The Last Time" Ozzel. The General tried to talk Vader out of killing him, so this is the second time that Glover had tried to prolong Sheard's life (well, save that Donovan wants the Grail for himself).
This isn't the first crusade that Julian Glover's character was involved in. He appeared in the Doctor Who episode aptly titled "The Crusade"
Dawson Casting: An inverted example. Allison Doody was 22 years old when Last Crusade was filmed, but she plays Elsa Schneider, who can be assumed to be at least around 30 years old considering that she's got a doctorate and she's a highly-respected art professor.
Fake Nationality: Welsh John Rhys-Davies plays Egyptian Sallah, Irish Alison Doody plays Austrian Elsa Schneider, English Alexei Sayle as the Sultan of Hatay and English Julian Glover plays American Walter Donovan with an impeccable accent (but listen closely to when he talks about Hitler and the Nazis wanting "write themselves into the Grail legend. Take on the world" and you'll hear his accent slip a little).
Seemingly averted, for once, with Sean Connery, famous for not even bothering with the accent; as near as anyone can tell it is apparently canon that Indy's dad really is a Scotsman.
Playing Against Type: Sean Connery, the original James Bond who spent most of his career playing tough, cunning heroes, here plays a squeamish "bookworm" who is not prepared for his son's rougher, tougher adventures - and he's absolutely hilarious in the part.
Real-Life Relative: Mrs. Donovan is played by Isla Blair, Julian Glover's wife in real life.
Reality Subtext: Sallah is quite surprised at Indy's true name and the origin of his nickname, "Dog? You are named after the dog!?". George Lucas indeed named Indy after his pet dog, who was also the inspiration behind Chewbacca.
Throw It In: "She talks in her sleep", was an ad-lib by Connery.
Under Age Casting: Sean Connery plays Dr. Henry Jones, Sr., father of Henry Jones, Jr., or Indiana Jones, who is played by Harrison Ford. However, Connery is only 12 years older than Ford (Connery was born in 1930, Ford in 1942).
In an early draft, the character of "Fedora" was going to be Abner Ravenwood, father of Marion Ravenwood, who was mentioned in Raiders of the Lost Ark.
It would appear that Sean Connery originally had a very different characterization in mind for Henry Sr., stating in a promo interview for the film that as Indy's father whatever Indy does "I did it first and I did it better." This initial characterization Connery pitched in the interview does not match up with the characterization in the film, where Henry Sr. is more of an Absent-Minded Professor and all around professional "bookworm", and while he does have his Genre Savvy moments, he spends much of the film fumbling and bumbling his way through the adventure.
Written-In Infirmity: Harrison Ford's chin scar, originating from an auto accident, is explained as coming from Indy's first experience using a whip, slashing his chin accidentally.
You Look Familiar: Ronald Lacey, who played Toht in Raiders of the Lost Ark, appears uncredited as Heinrich Himmler at the book burning. Incidentally, Michael Sheard, who plays Hitler, was the runner-up to play Toht.