The yellow classic automobile that Daniel polishes in the famous "wax-on/wax-off" training scene, then later offered by Mr. Miyagi as Daniel's birthday gift, was actually given to Ralph Macchio by the producer, and he still owns it. The car is a 1948 Ford Super De Luxe.
During the scene where Mr. Miyagi is drunk and celebrating an "anniversary," he reveals that he served in the 442nd Regimental Combat Team of the United States Army, an Asian American unit composed of mostly Japanese Americans (many of whom had been in internment camps) who fought in Europe during the Second World War and soon became the most highly decorated unit in the history of the American military.
According to the commentary track on the home video versions of the movie, William Zabka came up with a loose backstory for the Johnny Lawrence character, in order to better "get the feel" for playing the character. He states in the commentary that he envisioned Johnny as having no father, and that Kreese is the closest thing to a father figure he had in his life.
Mr. Miyagi's medal is the Medal of Honor, the highest military decoration awarded by the United States. It is easily recognizable by its blue ribbon and the inscription containing the word "valor." In real life, the 442nd Regimental Combat Team had 21 Medal of Honor awardees, including Senator Daniel Inouye of Hawaii. Its members also received 52 Distinguished Service Crosses, 560 Silver Stars, 4000 Bronze Stars, and 9486 Purple Hearts.
The legendary Toshirô Mifune auditioned for the role of Mister Miyagi. Although he was great in the audition (according to director John G. Avildsen in the DVD Commentary), it was felt that his version of Miyagi was "too serious" and played much like the samurai warriors he played in the Akira Kurosawa movies and he was turned down.
Martin Kove, who played the John Kreese character, was rumored to have replaced Chuck Norris, who allegedly turned down the role of Kreese because he didn't want karate trainers to be shown in an unsympathetic light. Norris has since said he was never offered the role but that if he had been, he would've declined for similar reasons.
According to Martin Kove in the DVD Documentary, he had gotten a call from John G. Avildsen stating that they wanted him to audition for Kreese but was then told to wait. Kove wanted the role so much that he turned down other prospects in order to get this part. But when the "waiting" dragged out for a few weeks, Kove became annoyed as he kept turning down parts. Finally when Avildsen called Kove in to audition, Kove was so annoyed at Avildsen that he berated the director and channeled his anger into an intense audition. Ultimately, that intensity got him the role.
According to Joe Esposito, "You're the Best" was originally written for Rocky III (1982) which explains the lyric "History repeats itself". The song had been rejected in favor of Survivor's "Eye of the Tiger". Ironically, Survivor also performed the theme song ("The Moment Of Truth") for The Karate Kid.
The referee in the final match is Pat E. Johnson, a karate expert and former student of Chuck Norris. He instructed many movie stars in karate. He is credited as the "fight instructor/choreographer" for the film.
The Karate Kid was the name of a character in DC Comic's "Legion Of Superheroes" who was a member of the Legion. DC Comics, which owned the name, gave special permission for the title to be used. There's a thank you to DC Comics for allowing the use of the name at the end of the credits.
Mr. Miyagi is named for Chogun Miyagi, who became the forerunner of karate-jutsu in Okinawa, Japan. 'Sensei Miyagi' as he was called, created his own style of karate-jutsu, which he dubbed 'Goju Ryu', which means 'hard and soft style'.
The Swedish liberal party Folkpartiet refereed to this film in their campaign during the 2010 elections: they proposed a mentoring program for young and new employees. One of their posters read: No Daniel-san without Mr. Miyagi".
Pat Morita was initially turned-down for the role of Mr. Miyagi because there was a "no comedian" policy when looking for an actor. He was later given the role because he was best for it after reading.
Former screenwriter Dennis Palumbo has said that he was offered the screen writing job for the film but reacted to the offer by saying he'd be "willing to do it if he (the title character, Daniel Larusso) lost the fight in the end." Palumbo explained his reasoning: "You can't have Mr. Miyagi tell him, 'It doesn't matter if you win or lose,' for 90 minutes and then have to have him win." Palumbo went on to say, "But that's because I was being a moron... Now, they made four sequels to that movie, so obviously I was wrong." (Palumbo's remarks appear in Tales from the Script (2009).)
Pat Morita's portrayal of Mr. Miyagi was heavily influenced by karate master Fumio Demura. Morita spent a lot of time with Demura, who doubled him for his fight scenes, and translated not only Demura's attitude towards the martial arts to the character, but also his mannerisms and speech.
Mr. Miyagi is depicted as a Medal of Honor recipient. Due to rampant racism among the U.S. Army's high command, no living Japanese-Americans were awarded the medal for service in World War II, and were given less prestigious medals instead. This was not corrected until an investigation in 2000, making Mr. Miyagi a Medal of Honor recipient in 1984 an anachronism.
According to black belt karate instructor William (Bill) J. DeClemente in "Black Belt" magazine dated May 1994, DeClemente believed he was the inspiration for The Karate Kid (1984) character. He was 17 years old when he started training in karate in 1963 in Queens, New York, the same neighborhood where screenwriter Robert Mark Kamen started training in karate in 1965. Kamen came to watch DeClemente teach in 1965 before enrolling at a karate school in Queens taught by Ed McGrath. Kamen has acknowledged in a sworn deposition that the tough ex-marine he depicted as John Kreese in the film was patterned after Ed McGrath, who was also a friend of DeClemente. DeClemente also said Kamen probably based Mr. Miyagi after Okinawan karate legend Chojun Miyagi. However, Kamen refused to acknowledge DeClemente as the basis of the karate kid character, in which DeClemente is the owner of the registered nationally trademark name "The Karate Kid" since the mid-1960s and was known locally in Queens, Brooklyn, and Florida and to his business associates. This led to DeClemente suing Columbia Pictures Industries, Jerry Weintraub Productions, and Jerry Weintraub on July 29, 1994 for trademark infringement, violation of his right of publicity claims, and seeking damages for three Karate Kid films. [Case: DeClemente v. Columbia Pictures, 860 F. Supp. 30 (E.D.N.Y. 1994)]. DeClement's case was dismissed, ruling in favor of the defendants. The court viewed the films did not damage the plaintiff, DeClemente, in a legal sense and that his public personality as the Karate Kid was not notorious enough that the public identified him exclusively with this persona as well as no evidence adduced that the defendants knew the plaintiff, until the year 1990. On his official website, DeClemente still maintains the claim that he is the inspiration for screenwriter Robert Mark Kamen of the films that bears his registered nationally trademarked name, "The Karate Kid".
When Daniel and Johnny are running out of the bathroom at the Halloween dance, an African-American student can be seen in a Spider-Man costume. Interestingly, in the Spider-Man comic book series following the death of Peter Parker in a 2011 issue, years after this movie came out, an half African-American, Miles Morales, took over the role of Spider-Man.