Actually, as far as I remember from the EU, Anakin lives at the Temple like everyone else. He just spends the night at Padmé's every once in a while without telling everyone where he was going. As a Knight, he's not monitored 24/5 unless there's been observable serious lapses in judgment (for instance, if the Council knew of the Sandpeople massacre, they'd be watching his every move). Really, though, other than a smart remark every now and then (which is a lot more common among younger Jedi, anyway), the Jedi Council isn't aware of any serious offenses on his part, so they don't have people spying on him.

As for not seeing that he was involved with Padmé, the catch-all answer for the Jedi not being more aware of their surroundings in the time of the PT is that Sidious was throwing the Force completely out of whack with his Dark Side juju. A poor excuse, I know, but it does emphasize how badass Palpatine was supposed to be, so I let it slide. Oh, and I doubt that the United States media would swarm over a pregnant senator if Washington had just been attacked and the President had narrowly avoided being taken hostage.

Of course, you can still blame GL for all of this, because he has a bad habit of leaving stuff for the EU authors to fix. It's a sad state of affairs when I admire the people who write the countless tie-ins more than the guy who created the entire franchise.