The Journal of the Whills
This gets into some serious, deep-cut Star Wars nerd stuff right here, but there is an Easter egg in Star Wars: Rogue One that dates back to the earliest days of the Star Wars universe when the whole thing was still just a script by George Lucas. In an early draft of Star Wars: A New Hope, there was an idea for an ancient book called The Journal of the Whills, Part I. This was eventually scrapped, but it is something that has occasionally showed up in the Star Wars expanded universe and has now been officially made a part of the new canon.
In the movie, Chirrut Imwe and Baze Malbus are casually referred to as part of a Force-believing group called the "Guardian of the Whills." This marks the first time the Whills have ever been mentioned in a Star Wars movie. It was said in the novelization of Star Wars: Revenge of the Sith that Qui-Gon Gin learned how to become a Force ghost from the "Shaman of the Whills," but we still don't really know who or what the Whills are. Perhaps now that it has been mentioned it will be explored further in a movie later on.
Saw Gerrera serves as an Apocalypse Now callback
Forest Whittaker's Saw Gerrera is a direct callback to Marlon Brando's deadly Colonel Kurtz in Francis Ford Coppola's surreal 1979 Vietnam War classic, Apocalypse Now. Saw is presented as a mysterious figure with the same type of leadership qualities. Mysterious yet powerful. And he has his own little cult that bends to his will. Apocalypse Now and A New Hope are inexplicably tied together. George Lucas helped his pal Francise Ford Coppola make the movie. And it was actually supposed to be Lucas' next project after American Graffiti. George wanted to make the war epic a simple low-budget, black and white pseudo-documentary alongside Coppola. But the pair couldn't get funding. So Lucas decided instead to develop Star Wars while Coppola went out and made Apocalypse Now, which is considered one of the all-time great war movies. Rogue One director Gareth Edwards has said he pulled inspiration directly from the Coppola film in making Rogue One.
The requisite THX-1138 callback
George Lucas' directorial debut was THX-1138, and it has been referenced in every Star Wars movie going all the way back to the 1977 original, with the detention block 1138 the destination for Chewbacca as Luke and Han cart the wookie away in disguise. The THX-1138 Easter egg might be a little harder to find in Rogue One. As Jyn and Cassian make it to the top secret data facility holding the Death Star plans, Cassian must manually extract the data tape housing the Death Star schematics. Doing this, he uses a pair of clamps that are almost identical to clamps used by the hero in George Lucas's debut feature film.