During the original Karate Kid shoot, late director John G. Avildsen shot hours of tournament footage from multiple angles. The crew behind Cobra Kai searched the studio vault and found a ton of never-before-seen clips, which they were able to introduce into the series via flashbacks. One of them includes Zabka's real life mom, who was in the stands in different angles that went unseen until 2018. Ralph Macchio told Uproxx there are three brand new angles of the famous crane kick.
The headband that Daniel wears when he decides to train karate again, is the actual headband from The Karate Kid (1984). It was given to Ralph Macchio after the completion of the first film.
Daniel's car in season 2 is the actual same car from The Karate Kid (1984). It was given to Ralph Macchio after the completion of the first film.
Over the years, many Karate Kid fans joked that Daniel was the real villain of the first movie, while Johnny was mostly just defending himself and/or retaliating to Daniel's antics (for example, there's this take on Daniel's actions from J. Matthew Turner). In this series, it's shown that that's exactly how Johnny sees the events. The series doesn't cast either man as a simple villain, but shows that both are flawed and often blinded by their own assumptions, and who's the hero is often a matter of perspective.
Ralph Macchio was 56 years old at the release of this series - four years older than Pat Morita was at the time of release of The Karate Kid.