In no particular order...
I was really amazed at the number of people who were frustrated with the amount of time that it took the BBC live special to get around to telling us that Peter Capaldi had been cast as the Twelfth Doctor. After all, they could guarantee that people would stay tuned in until the name was mentioned. After that, they could reasonably expect most people to turn off their sets. Is it any surprise that they waited until about twenty-eight minutes into the thirty-minute special to mention the name? And everything that led up to it was about what I expected, a low-key celebration of How Awesome Doctor Who Is, with a bunch of random talking heads from the series reminiscing. Anyone getting highly upset over the special needed better expectation management skills.
At this point, I expect a full, written apology from everyone who insisted that they'd totally heard from someone inside the production team that David Tennant was coming back because Matt Smith had done such a bad job with the part. Written in your own blood, preferably.
I have to admit, Peter Capaldi does look and sound exactly like the sort of actor you'd expect to play the Doctor. Not famous, but having built up a respectable body of work. Not glamorous, but charming and witty. Quirky and unusual, with a reputation for taking a part and making it his own. Eccentric as all hell. If you were to template the "Doctor Who actor" persona, it'd probably be Peter Capaldi. I expect he'll do well in the role, although as with pretty much everyone they've announced, I'll need to see him actually playing the part with live scripts and everything before I can really get a feel for him. (After that, it usually takes me about five minutes to settle in and decide that yes, this is the Doctor. For Matt Smith, the exact moment when I knew he was going to be brilliant was when he said to Caitlin Blackwood, "You know how sometimes adults tell you that everything is going to be just fine, and you know they're lying, but they say it anyway to reassure you? Well...everything's going to be just fine." Delivered not in a tone of reassurance, but with a manic glee that made it perfectly clear that he loved not knowing whether things were going to be fine or not.)
I am not one of the people, by the way, who was rooting for an older actor in the part. I feel like the Doctor should be someone young or at least youngish, because regeneration is a process of physical renewal and it makes no sense to me that Matt Smith's body is going to transform into Peter Capaldi's in a process of bodily renewal. I feel like the Doctor should get his money back for this body. (It's worth noting that the only times the Doctor has ever regenerated into a conspicuously "older" body, Pertwee and Eccleston, we didn't see the transition onscreen. I still think that there were decades of adventures of a younger Pertwee Doctor that we never saw.) That said, I'm clearly overruled here.
My one big disappointment with the whole process so far is finding out that Moffat made no serious attempts to audition anyone other than Capaldi. Given his statements that he believed a female Doctor or a minority Doctor would only work if it wasn't a stunt and the actor/actress in question legitimately won the part, it seems hypocritical as all hell to decide not to give them the chance because he'd already settled on the white male he wanted. I do feel that Moffat has a problem with gender essentialism--the "Men Are From Mars, Women Are From Venus" bull-hockey that evo-psych majors peddle to CNN on a slow news day--and I think that he just couldn't see casting a Doctor who wasn't a "traditional" Doctor as anything other than a gimmick.
Which is a shame, because I really feel like this would have been the perfect time for it. He needed to cast against Smith, so it needed to feel like a big change, but at the same time Smith was who his instincts were telling him was the best for the part, and deliberately going against your own instincts can result in some very bad decisions. (Colin Baker was molded as "angry, loud, and annoying" because it was the opposite of Davison's "charming, friendly and happy," without realizing that those were traits unlikely to keep an audience.) I think that a female Doctor, or a minority Doctor, would have been a very effective "pattern break" that would have given Moffat something completely different to do with the character and avoided repetition without having to consciously avoid repetition. And also it's the right thing to do after loudly and publicly insisting that the Doctor is a role that's color-blind and gender-neutral, because saying all that and then not auditioning a single non-white-male actor for the part makes you look like a lying bastard and not in the usual cute way that it does when you lie about how exciting the season finale's going to be, but that's going to be true anytime. This felt like the right time for a change beyond just "white man to white man", and I'm disappointed that it didn't happen.
Still, that disappointment will probably last until about five minutes into the Christmas special, when Peter Capaldi will show us all why there's never been a bad choice for the Doctor. Bad scripts, bad writers, bad script editors, bad directors and bad producers, yes. But never a bad Doctor.