Weirdly enough, I have less of a problem with this than I do with the "half-human on my mother's side" thing.
"Half-human..." came out of nowhere - it's the Doctor, who's *never* indicated that he was at all human, ever, not once, in the history of the show, suddenly revealing something to a total stranger. Granted, maybe it explains why he loves Earth so much, but it just plain doesn't make sense. I could get really nerdy and say "if he's half-human, then how did William Hartnell know it was 'far from being all over' - surely he'd be afraid that he wouldn't regenerate - but mostly it's because it goes against the grain of the show. If there's one thing we KNOW, as viewers, it's that the Doctor is an alien. Whether that means he's a mysterious figure, like he was early on, or whether that means he's a Time-Lord-From-Gallifrey... he's an alien. We thought we knew that, and now here's some stupid American show (made in Canada, of course) telling us he isn't. Bleh.
Rory and Amy making a Time Baby with a Time Head, however... one thing we learned this past season - and this was a recurring theme, if you paid attention - is that the Doctor doesn't know everything, least of all about the TARDIS. For whatever reason, the mere fact that Matt Smith was acting surprised at that moment makes it okay with me. Don't know why.