0:40 - Narrator: "Now, having passed the test, they take their first step into a larger world." Speaking to Luke, Obi-Wan uses the same expression in A New Hope: "You've taken your first step into a larger world" [1:02:36].
3:19 - Huyang (to Gungi): "Concentrate." Yoda also says this (to Luke) in The Empire Strikes Back [1:08:40 and 1:16:38].
3:43 - The top of Huyang's podium has the same basic design as EV-9D9's in Return of the Jedi [11:16]:
7:11 - Ahsoka (to R2): "Get us out of here." In A New Hope, Han Solo also says this (to Chewbacca): "Chewie, get us outta here!" [55:26].
14:00 - Petro (after a pirate asks the younglings to hand over their crystals): "Over my dead body." Han Solo uses this same expression in A New Hope [50:42].
17:41 - Ahsoka: "Hondo, the Jedi council will not take kindly to this attack." There's some similarity between this and what Leia says to Vader in A New Hope: "The Imperial senate will not sit still for this" [7:41]. The context is basically the same, too: a ship has been boarded.