0:37 - Commandant Aresko (to the cadets): "By the time you complete your training, you will be prepared to serve your emperor." Vader uses the same expression in The Empire Strikes Back when he tells Luke, "Join me, and I will complete your training" [1:50:39], and the Emperor uses it in Return of the Jedi (also speaking to Luke): "I am looking forward to completing your training" [1:31:04].
17:42 - Jai Kell (after a tank fires at the walker they're inside): "Fire back!"
Zare Leonis: "I'm trying!"
Leia gives the same response to Han in the trash compactor in A New Hope [1:23:41]; Han says, "Get on top of it," and Leia replies, "I'm trying!"
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The symbols that the cadets have on their helmets (and the helmets themselves) are reminiscent of a Ralph McQuarrie concept painting for The Empire Strikes Back:
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