Rose met the most fantastic man in the universe, who actually thought she was the most fantastic woman in the universe and that doesn’t really happen often.
On hearing from Tasha Lem that everyone in the church was trained to see through holograms, Clara originally added “Well isn’t that just…beezer!” After the Doctor handed Tasha his key to the TARDIS, he rounded on Clara and asked, “Beezer?” “Thing my Dad says,” explained his companion. “Nobody says beezer,” claimed the Time Lord. “They used to,” retorted Clara. “I’m a time traveller, they really didn’t,” insisted the Doctor.
Returning to the town, on emerging from the TARDIS Clara commented on how good it was to be wearing real clothes again, with the Doctor replying, “No idea. I couldn’t see your hologram clothes, I have a sublight astigmatism.” As the Doctor walked on, Clara paused, saying to herself “…Beezer.”
Deleted scenes from The Time of the Doctor, in Doctor Who Magazine’s Guide to the 50th Anniversary.
So, erm, yeah, the Doctor saw Clara naked.