A) It would be very hard not to notice that Ahsoka didn't have her lightsaber. Her not wearing a Jedi robe should make it pretty obvious.
Her not wearing much of
anything should make it pretty obvious.
But Anakin is the kind of guy who gets blinded by his own agenda and concerns so I could buy it.
Except that it seemed she was by his side for a considerable length of time, all the way from the bar back to the Jedi Temple. He would've had to be
really preoccupied with something not to notice. And the guy's a trained warrior -- his survival depends on noticing the details of his surroundings. I can't believe he could be so preoccupied that he wouldn't notice something that was so close to him for such a significant length of time, especially when it's something as important as a lightsaber, something he's repeatedly lectured Ahsoka about.
I would assume that for a warrior it's a matter of reflex, essentially, to be aware of any weapons being carried by anyone nearby, friend or foe. By analogy, I'm a writer, and I notice written words everywhere; by reflex I read anything in my field of view. Words are my tools; I'm trained to be hyperaware of them. So I expect that a warrior or soldier would have a similar reflex for "reading" weapons in his or her vicinity, and with far more urgent motivation for doing so. I think Anakin would be more likely to overlook the absence of Ahsoka's tube top than the absence of her lightsaber.