A fan on another board suggested that Anakin should throw away his Jedi lightsaber when he says "What have I done..." indicating that he is not worthy of being a Jedi. Maybe later, Sidious would give him the Darth Vader lightsaber, followed by Anakin's line "Thank you my master". (originally from the first scene)

It should be implied that Yoda would find Anakin's Jedi lightsaber on Coruscant. Yoda would later give it to Obi-Wan saying "Pass this on when the time is right". The latter scene might be hard to get.. but it would solve a few problems.

The Sith knighting ceremony is transferred to the hologram that Obi-Wan and Yoda watches in the Jedi recording room. The long "Darth ... Vader" with pause in the middle is replaced with Ian McDiarmid saying "Darth Vader, Dark Lord of the Sith" from the "Musical Journey" DVD (came with soundtrack).