I may be in the minority, but I loved the card gag. It was predictable, but go back and see what was written on some of the other cards they flipped through.

The visual joke Dean Winters pulled off- flicking his smoke into the fountain after lecturing Jake about respect for church- absolutely needs to be recognized.
It was executed as perfectly as the best Seinfeld visual stuff.

I don't think she comes off as dumb at all- she comes off as wary. Wouldn't you be if the person you were stuck with was trying simultaneously to both save and kill you?

I suspect we may find that not only is Missy's "dying is for other people" very important to her and Clara in part 2, it might also end up being a recurring theme throughout this season.

Is this the first time it's been officially recognized that a male Time Lord can regenerate as a female?

That was Foxes who had a fairly big hit in the US with the DJ/Producer Zedd.