4:06 - Clovis (to Padmé): "I need your help." Queen Amidala says the same thing to Jar Jar in The Phantom Menace ("I need your help" [1:37:55]); Obi-Wan to Padmé in Revenge of the Sith ("Padmé, I need your help" [1:38:44]); and Obi-Wan to Luke in A New Hope ("I need your help, Luke. She [Leia] needs your help." [36:03]).
4:11 - Clovis (after Padmé says, "Last time you needed my help, I ended up poisoned, and you did nothing"): "That's not true." Luke says the same thing in The Empire Strikes Back when Vader tells him about his father: "That's not true. That's impossible." [1:51:21].
6:50 - Palpatine (to Padmé, about Clovis): "Perhaps then, in this scenario, it would be best for you to trust an old friend and do what he suggests." The phrase "old friend" is also used in Attack of the Clones (where Palpatine suggests "an old friend, like Master Kenobi" to protect Padmé [6:34] and Count Dooku calls Mace Windu "my old Jedi friend" [1:50:24] and just "old friend" [1:56:05]), in Revenge of the Sith (where Obi-Wan says, "Goodbye, old friend" to Anakin as he leaves for Utapau [51:13] and Yoda refers to Qui-Gon as "an old friend" [2:09:56]), in A New Hope (where Leia sarcastically says, "We, uh, ran into some old friends" when Han asks her and Luke where they've been [1:31:33]), in The Empire Strikes Back (where Yoda says that through the Force, Luke will see "Old friends long gone" [1:17:05]), and in Return of the Jedi (where Luke says, "I have a promise to keep to an old friend" [37:37] and Han calls C-3PO "an old friend of mine" [1:11:53]).
12:43 - Muun: "What happened to the lights? I can't see a thing." Obi-Wan says the same thing in Revenge of the Sith, after the cockpit of his starfighter fogs over ("I can't see a thing" [6:11]), and Luke says the same thing in A New Hope about his stormtrooper disguise ("I can't see a thing in this helmet!" [1:13:17]) and in The Empire Strikes Back while entering Dagobah's atmosphere in his X-wing ("All the scopes are dead; I can't see a thing" [41:09]).
12:51 - Muun (talking about the downed electrical system): "Power has been cut, and the security lock is engaged. It will take some time to switch over." Speaking about Leia, Vader uses a similar expression in A New Hope: "Her resistance to the mind probe is considerable; it will be some time before we can extract any information from her" [51:15].
13:26 - Mak Plain: "Where is the senator?"
Clu Lesser: "We got separated in the darkness."
Padmé: "I'm here."
There are similarities here to two scenes in Return of the Jedi. On Endor, Han asks Luke, "Where's Leia?" and Luke explains that "We got separated" [1:02:15], and earlier, in Jabba's palace, after Han asks, "Where Leia?" she replies, "I'm here" [28:41].
14:35 - Nix Card (to Muun guards who arrest Padmé): "Take her away." In The Phantom Menace, Nute Gunray commands, "Take him away," to a pair of battle droids, referring to Sio Bibble [1:18:19], and in Attack of the Clone, Jango Fett says, "Take him away" to battle droids, referring to Anakin [1:42:30].
14:44 - Padmé: "I have powerful friends." Leia says almost the same thing to Jabba in Return of the Jedi: "We have powerful friends" [21:02].
15:07 - Muun (to Anakin): "This way, Master Jedi." This same direction is given in The Phantom Menace (by TC-14 to Qui-Gon and Obi-Wan: "This way, please" [2:45]) and in Attack of the Clones (Taun We to Obi-Wan: "Now, please, this way" [42:07]).
15:14 - There are two visual references to A New Hope in this shot:
Anakin's silhouette on the wall resembles that of Darth Vader, and Padmé's pose is similar to that of Leia on the Death Star [1:15:58]:
15:19 - Padme: "Ani, I'm so glad to see you." Luke uses a similar expression in A New Hope: "Ben Kenobi? Boy, am I glad to see you!" [30:35]
21:20 - Darth Sidious (to Embo, referring to Anakin, Padmé, and Clovis): "From this point, I will deal with them myself." In Revenge of the Sith, General Grievous says, "I will deal with this Jedi slime myself," referring to Obi-Wan [58:03], and in Return of the Jedi, Vader says, "I will deal with them myself," referring to the Rebel strike force [56:10].
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At 16:07, there's a brief musical cue of the Imperial March as Anakin becomes upset after Padmé mentions Clovis.