The Mandalorian Armorer (Emily Swallow) mentions an ancient band of sorcerers known as the Jedi. As she tells Djarin, the Mandalorians once waged war against the Jedi. This war, which occurred thousands of years ago, has been referenced a few times in Star Wars: The Clone Wars (2008) and Star Wars: Rebels (2014). It's been said that it was this clash with the Force-using Jedi that caused the warriors of Mandalore to develop the armor and weapons that they continue to upgrade and use today.
Cara Dune's full name is Carasynthia Dune. Her home planet is Alderaan, the same planet that Princess Leia Organa called home and the same planet that the Death Star blew up in Star Wars: Episode IV - A New Hope (1977). This background explains why Dune was so eager to help the Mandalorian the instant she found out Nevarro was lousy with Imperials. She doesn't just have a Rebel soldier's hatred of Imperials; she has an Alderaanian Rebel soldier's hatred of Imperials.
The two Stormtroopers comically failing at target practice is an in-joke aimed at the notoriously bad marksmanship displayed by Stormtroopers throughout the original Star Wars trilogy. This originally started as a running joke among fans of the film series, but was eventually acknowledged in-universe in Chapter 6: The Prisoner (2019).
Moff Gideon is described as "an ISB officer during the purge". The acronym stands for Imperial Security Bureau. This means he was one of the Emperor's agents who served as a mix of spy, torturer, and officer who watched the Imperial ranks for signs of sedition. Another agent of the ISB was Alexsandr Kallus from the Rebels animated series.
The Armorer says Mandalore the Great fought against "an order of sorcerers called Jedi." As well as being the name of their planet, the word Mandalore can refer to the leader of the group. In Legends, "Mandalore the Ultimate" waged a war against Jedi in the ancient Old Republic times.