Mace Windu was willing to execute Palpatine on the spot, because he recognized that Palpatine was "too dangerous to be kept alive", and feared both Palpatine's influence on Anakin, and his influence on the Senate and Courts.
Was this decision for a summary execution on the spot in keeping with the Jedi way, or was Mace's decision influenced by his use of the Vaapad fighting style?
(both quotes sourced from IMSDB), first one when Anakin dis-arms (and dis-hands) Dooku, then kills him:
ANAKIN: ... I couldn't stop myself.
PALPATINE: You did well, Anakin. He was too dangerous to be kept alive.
ANAKIN drops COUNT DOOKU's lightsaber, moving to PALPATINE.
ANAKIN: Yes, but he was an unarmed prisoner.
ANAKIN raises his hands toward PALPATINE, who is strapped in the Admiral's Chair. The Chancellor's restraints pop loose.
ANAKIN: (continuing) I shouldn't have done that, Chancellor. It's not the Jedi way.
And the second one just before Anakin's fall to the Dark Side:
MACE WINDU: You Sith disease. I am going to end this once and for all.
ANAKIN: You can't kill him, Master. He must stand trial.
MACE WINDU: He has too much control of the Senate and the Courts. He is too dangerous to be kept alive.
PALPATINE: I'm too weak. Don't kill me. Please.
ANAKIN: It is not the Jedi way...
Yet Mace Windu was clearly willing to kill Palpatine, even though Palpatine was apparently beaten. This was discussed in a separate question, and I think the answers provide some good explanations for Mace Windu's motivation.
My first thought was that Anakin, a Jedi Knight for a mere three years, and teetering on the edge of falling to the Dark Side, would not understand the Jedi way as well as Mace Windu, Jedi Master and member of the Jedi High Council.
But then I noticed this from one of the answers:
Also, Windu practices and mastered a lightsaber technique call Vaapad, that channels your rage into your strikes in a controlled manner. If anything there is/was a lot of darkness within him, which it fought to control.
I found that interesting, and looked into that a bit more on Wookieepedia, which had this to say:
Vaapad was described as more than a fighting style; it was a state of mind that led through the penumbra of the dark side, requiring the user to enjoy the fight, and relish the satisfaction of winning. The practitioner of Vaapad would accept the fury of their opponent, transforming them into one half of a superconducting loop, with the other half being the power of darkness inherent in the opponent. The form was also mentioned with a cautionary warning by the Jedi that use of Vaapad led the user perilously close to the dark side due to its focus on physical combat.
So given that Mace Windu was using this form at the time of his decision to kill Palpatine, was he really making a decision in keeping with Jedi ideals, or was this the fury of "the penumbra of the Dark side" tinging his judgement?
Is killing an apparently beaten foe justifiable under the Jedi ideals, or are the precedents for immediate and summary execution?