First of all, lets get this out of the way:
I know that a lot of people are having some trouble wrapping their heads around the idea of Peter Capaldi as the new Doctor, for a number of reasons. The biggest, I think, is that we as fans never want to see the character/actor that we've come to love change in the very unique way that the Doctor does. Yes, he's still essentially the same man, at his core, but realistically, he isn't. The history remains, but a new actor steps in, assumes the name, and goes about being someone new, untested, untrusted. We love the Doctor, we don't want anyone to muck about with him. I was HORRIFIED when Eccleston changed into Tennant, utterly convinced that I wasn't going to like him AT ALL. Then Tennant ended up becoming my favorite (not just Doctor, but one of my favorite ACTORS. He's bloody brilliant in everything I've seen him in. Seriously.) I cried like a leaky sieve when Tennant stepped aside for Smith, and I hated Smith for the bulk of his first season. But now I'm sad to see him go. It's part of the cycle that fans willingly accept when they join the Whovian ranks. So, I caution my fellow Whovians, give it a chance. Take a deep breath, remember that it's probably going to be fine if for no other reason than DW has become the BBC's flagship internationally, and they aren't going to risk cocking it up by casting someone terrible.
I also know that a lot of people are upset because he's had two previous roles in the Whoniverse already. One, maybe, wouldn't be too bad. After all, Freema Agyeman, Karen Gillan, Eve Myles, and even our beloved David Tennant had roles in the Whoniverse before they became main characters. (Yes, even David Tennant. He voiced the Caretaker in the animated Doctor Who: Scream of the Shalka in 2003, 2 years before becoming the Tenth Doctor. And was uncredited!) But two, with his role as John Frobisher in Torchwood being such a large role, and many people may have trouble disassociating him. My thought is this: The man obviously LOVES Doctor Who, or he wouldn't have accepted two roles, let alone that of the titular character. And who better to take over than someone who obviously is such a fan himself? (Oh, and did we all see where he wrote a letter to the BBC many years ago about Doctor Who? He's been a Whovian for over 40 years!
Check it out if you haven't already seen it.)
Some people (likely the younger, female crowd) are unhappy because he has no sex appeal (I am directly quoting a Tweet I saw earlier today). I say, who the hell cares? First and foremost, if you don't know anything about the actor, you can't really judge his appeal. I almost got into fisticuffs with my own mother last week because she repeatedly told me during an argument about casting that Tennant was unattractive. I find him distractingly sexy, but I know that the tall, lanky, pale, geek chic isn't for everyone. Part of what I love about him, part of what I find so attractive, is HIM. His personality (both in real life and the life he gives to his roles), and his ability to take a role and make it completely his own. Who's to say that after we see Capaldi in action we all won't be steadfastly declaring him to be a Silver Fox? But that, ultimately, is neither here nor there. The man was cast because he can act, and obviously the people who make these decisions decided that he would fit the role well. (And yes, people will say it was Moffat, and curse and shake their fists, but really, if he was just dead terrible and an embarrassment to watch, I have a sneaky suspicion that there's someone above Moffat who could veto that decision.)
Some people desperately wanted Twelve to be an actor of color, or a woman, or of alternate sexuality (though I don't really see what that last has to do with anything at all). I understood both the call for change, and the hesitations voiced by some. If the Doctor changed race, I feel that his race would always be brought to the forefront (remember how Shakespeare repeatedly commented on Martha's skin tone?). And that would ultimately distract from the heart of the show. If the Doctor became a woman, the same could be said. The unfortunate truth is that anytime the Doctor went into the past as either a person of color or a woman (at least on Earth) some of the authority and freedoms that he's granted would be lost. James K. Van Fleet once said "I'm always willing to accept change, just as long as it isn't change for the sake of change. If that change will result in a better way of doing things, then I'm all for it." And I don't know if we as a world-wide community are READY for such a change in our cultural icons. Not when things like race, gender, orientation, and belief systems are still such hot-button issues in our societies. Give it time, maybe if DW continues for another 50 years (which it very easily could) all of these changes will be seen.
Casting Capaldi might also very likely change the interactions between the Doctor and his companion (Clara, for now.) I admit to coming into the Who fandom with Eccleston. It was actually recommended to me that way: start with the newer ones and fall in love, then when you go back and watch the classic episodes you won't care that they're in black and white and the effects are terrible. It's how I recommend the show to people. So it's only in my delving into the classic episodes that I can come across the Doctor and his companion without that blatant romantic overtone that seems to color the newer series'. I'll also admit that I'm a huge Doctor/Rose shipper. I think they had unmistakable and brilliant chemistry, but I remember being irritated with Martha always pining after him, and refreshed that Donna didn't seem to give two flying leaps about him as anything other than a best friend. Amy's advances on the Doctor on the eve of her wedding made me instantly dislike her (I personally thought the show would have been more fun to watch if only Rory had gone along) and I was never comfortable with River and the Doctor for reasons I can't quite put my finger on... though it likely has something to do with the aforementioned ship. I liked the episodes that had the Doctor and Clara just palling around, but there were some that seemed to have them leaning into a romance that I wasn't as fond of. I personally hope that Clara and Twelve won't have any romantic chemistry! I want to see them interact like friends, or as an elder showing the younger the delights of the universe! I hope that Capaldi will be able to keep up with the blazingly high standards set forth by the three most recent actors, and still tap into the classic frame of mind. And I, personally, think that he will. He'll be Fantastic! Molto Bene! Brilliant! We, as fans, just have to give him a chance.