Sorry about not commenting on the scene before but I needed a bit of time to think about it.
There are a few key problems with it both largely stemming from the way Mace Rimmer...sorry Windu is written.
He is always on Anakin's back from the first day they met and yet Anakin (or at least so we are led to believe) feels remorse for his part in killing him (in the same 'golly that was a bit naughty of me' way he does with Dooku but remorse none the less).
There was a missed opportunity here not only for allowing Mace to explain that his actions stemmed out of caution and care for Anakin, creating more conflict in Anakin because he suddenly sees a different side to this strict git who never made him feel welcome and really was holding him back (in all the ways he argues Obi-Wan was in AOTC even though we saw little evidence for this back then).
Instead Mace continues in that vein (making him sound even less sympathetic).
Anakin has just risked his life and his ambitions to give Windu a warning about Palpatine and all he does is say "If you aren't lying to me I will then trust you, until then I don't trust you enough to be around me".
I don't know Sam Jackson's films enough to know if it's possible to cobble together the sort of scene I'm thinking of here.
Essentially I would have Anakin tell Mace that Palpatine is the Sith Lord.
Have Mace thank him, tell him he HAS earned his trust and say something along the lines of up until then they didn't know who to trust and because of Skywalker's abilities they had to be careful around him up until that point as he was the only hope in defeating the Sith.
I would then have him say that as only the arresting Jedi and Skywalker know who Palpatine really is Skywalker should stay behind if things go wrong, to warn everybody else and not stick all their Jedi eggs in one basket (instead of I don't trust you to do the job properly and you may be lying).
That way Mace is putting himself in harms way to protect Skywalker and the Jedi as a whole rather than trying to steal Anakin's thunder and take him down another peg.
Anakin's dilemma then becomes one of "Do I do my duty to the order or try to protect my wife?" instead of "He's always holding me back, I'm the bleedin Chosen One, Mace doesn't trust me and Palpatine is probably right about the Jedi being just as bad but not as much fun".
The alternative is to drop the conflict altogether and have Skywalker knowingly drop Mace right into a trap (and be a bit pissed off that Mace isn't entirely falling for it).
When Mace does what he does it could be the vindication of everything Palpatine has said (because he is telling the truth).
In which case the scene needs to be edited to be if anything more snarky...Anakin is playing Iago here (giving Palpatine a bit of a rest) and creating a crucible to iron out the true nature of his warring mentors.
His scene in the council chamber would then become (instead of a "shall I shan't I?" scene) an epiphany (the Jedi aren't good after all, everyone is just as screwed up but at least Palpatine is offering me something I need).