1:04 - Anakin: "We're gonna have to fight our way off this rock." In A New Hope, Luke disdainfully refers to Tatooine using the same expression; after C-3PO asks if there's anything he can do to help, Luke replies, "Not unless you can alter time, speed up the harvest, or teleport me off this rock" [19:58].
3:15 - Sobeck (to Dooku, about the hyperspace coordinates): "I will see to it that they are soon back in our possession." While the specific diction is a bit different, Vader says something similar in A New Hope during a meeting on the Death Star: "The plans you refer to will soon be back in our hands" [37:52].
4:00 - In the background of this shot, Commander Cody jumps on top of a crab droid and fires his blaster into it. In Revenge of the Sith, an-other clone trooper does the same thing [1:20:01].
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6:34 - Anakin (to Ahsoka, discussing the Jedi's role in the war): "But we aren't soldiers; we're peacekeepers." Mace Windu also says this in Attack of the Clones, although slightly differently: "We're keepers of the peace, not soldiers" [4:49].
6:49 - Ahsoka: "Did you hear that?"
Even Piell: "Yes, we're going to have company."
Both of these lines also appear in A New Hope. At the beginning of the movie, C-3PO asks R2-D2, "Did you hear that?" [2:47] (incidentally, this is the first line of dialogue), and later, Han yells, "Luke, we're gonna have company!" [1:15:46].
7:13 - Sobeck: "Tighten your grip, K2-B4." Leia uses this same expression in A New Hope: "The more you tighten your grip, Tarkin, the more star systems will slip through your fingers" [57:44].
12:35 - Sobeck: "I will deal with this personally." It's probably coincidental, but this seems to combine Grievous' line "I will deal with this Jedi slime myself" in Revenge of the Sith [58:03], Vader's line "See to it personally, commander" in A New Hope [8:42], and Vader's "I will deal with them myself," referring to the Rebel strike force, in Return of the Jedi [56:10].
16:05 - Wilhelm scream (Clone trooper)
20:36 - There's a brief musical cue of the Imperial March as Tarkin and Anakin shake hands.