They just do it so all the losers can have something to talk about.
Look at one point during the pod race Sebulba isn't even in his pod there is no one driving it. they probably see it and figure they can get away with it, and they can for the normal people, but the nut jobs that view frame by frame will catch it.
It's not that weird.
When the scene was originally shot, Anakin was already in the office when the Jedi arrived to arrest Palps.
Palpatine used Anakin's saber for the duel.
That was why the Palps figure came packaged with Anakin's saber.
The scene was reworked extensively in late 2004.
As well as Ani entering at the end of the confrontation, and Sidious now using his own saber there were a number of changes made at different stages.
At one point Palpatine revealled Plagueis was real during the duel, as he was pleading with Anakin.
At one point Palpatine's saber was cut in half by Mace rather than booted out of his grasp.
In the animatics, Anakin cut Mace's saber in half rather than going for his arm. Mace tried (and failed) to repel the final bout of lightning with his hands.
And on top of all of this, much of the actual fight was actually cut altogether, particularly at the start of the duel.
With so much footage to choose from, this shot obviously either got in by mistake, or GL probably thought that the take was good enough to warrant the minor continuity error.
I mean, it took is nearly a month to spot it. 😛
Well spotted, The Anomaly...