Star Wars Episode III: Revenge of the Sith Chapter VIII: Bad Dreams
The view of Amidala's apartment complex reveals its veranda on the right-hand side. In Episode III, this location was newly-added to the building established in Episode II. In that film, the apartment was not seen from an angle that could reveal the absence of the veranda, so it was stated in-continuity that it had been part of the apartment all along.
Padmé is still wearing the japor snippet necklace Anakin gave to her after leaving his mother in Episode I.
Padmé specifies that she wants to have their "baby" on Naboo, revealing that the couple does not yet know Padmé is pregnant with twins. The novel establishes that Padmé ordered her medical droid "not to spoil the surprise" of the baby's gender. 
Anakin's mechno-arm is seen fully here, and has been upgraded since last seen on film in Episode II. The circumstances of this upgrade are detailed in Clone Wars Chapter 25, where Anakin's arm is destroyed during an attempt to disable a Techno Union laboratory on Nelvaan. Anakin later replaces it with the black-and-gold prosthetic seen here.
The entrance to the veranda is actually located through a walk-in closet in Padmé's bedroom.  When the decision was made to add a veranda to the apartment for Episode III, the only logical place to position the entrance was through what had been, in Episode II, a closet. The novelization states that its original function is still intact. 
The "Queen" mentioned here is not Jamillia introduced in Episode II, but Queen Apailana, who replaced Jamillia after the latter's four-year term. Apailana only reigned for a further two years before she was assassinated by members of the Empire's 501st Legion.  This event is part of the "Rise of the Empire" campaign in Star Wars: Battlefront II.
"Anakin's Dream" follows the initial establishing shots of Galactic City. This is track two of the Episode III original soundtrack, and continues through Anakin's vision and the veranda scene.
A snippet of "Anakin's Theme" from Episode I can be heard as Padmé approaches Anakin.
- ↑ Star Wars Episode III: Revenge of the Sith novelization (Matthew Woodring Stover, 2005), p217 (hardcover)
- ↑ The Official Site: Set Diaries: All the World's a Stage
- ↑ Star Wars Episode III: Revenge of the Sith novelization (Matthew Woodring Stover, 2005), p166 (hardcover)
- ↑ The Official Site: Databank: Queen Apailana