In his Chancellor "disguise" he's practically channeling Dr. Evil ("sharks with frickin' laser beams attached to their heads!"). I can't imagine anyone who couldn't see it a mile away even if they didn't already know and it seems to be very intentionally shot that way. There's no mystery at all, which also makes Anakin look like even more of a complete moron and ruins his character arc.

As a viewer it doesn't work at all, but I try to tell myself that Palpatine is just so powerful that he can blind every Jedi, every Senator and eveyone else in the galaxy. Unfortunately, it was so poorly executed in the script and on screen that it becomes impossible to suspend disbelief, so the intended drama and character development just falls flat.