Regarding the Doctor and Leonardo, don't they interact in City of Death?
Nope and that was the second time the fourth Doctor failed to meet him, but he did leave him a note telling him to paint over the writing anyway.
I love that bit. I keep hoping for some reference to that on the new series. Like, in "The Girl Who Waited," when Rory sees that Mona Lisa in the alien art gallery, I wanted the Doctor to ask Rory to give it a quick X-ray scan with the sonic. Rory sees "This is a fake" written on it, to which the Doctor promptly responds, "Oh, so that's the real one then."
Interestingly, although we would assume that the Doctor has in fact met Leonardo da Vinci, it seems that, in "City of Death," the Doctor was lying about having met Shakespeare, since the 10th Doctor has never met him before in "The Shakespeare Code." (But then, that doesn't jive with the fact that the 8th Doctor actually met him in the Big Finish audio "Time of the Daleks.")