A major spoiler is revealed, so click away if you want to avoid that.
Let's get this out in the open at the beginning; Peter Capaldi is already an amazing Doctor. He is literally the best possible candidate to embody the classic and rebooted series and take it into its second 50 years of life. It is impossible not to see what made Tom Baker's first several seasons so memorable in Capaldi's mannerisms, but there is also that iron edge of Eccleston's that captured a new audience. In Capaldi's Doctor there is little fault.
Little, but not none.
Of all the post-regeneration episodes I would say that "Deep Breath" does the worst job of introducing us to who the new Doctor is. There's none of the quiet strength of Troughton in "Power of the Daleks", or the tenderness seen in "The Eleventh Hour". I would argue that even McGann's movie is a better how-do-you-do to the new bloke than "Deep Breath".
First of all, they spend entirely too much time on the confused shenanigans following the regeneration. Capaldi stumbles around compellingly, but with incredible silliness far longer than is necessary. Tennant got more done asleep than Capaldi gets to do in terms of total running time.
Even when he's up and about there's still a hesitancy to really commit to a new incarnation. Half of his lines sound like they could have come right out of Smith's mouth, making you wonder what the point was in even switching them. Only in the last act does the Twelfth Doctor stand tall on his own as a new man.
On the plus side is Clara, who is finally getting some real character development outside of being last season' living MacGuffin. I've heard a rumor that Steven Moffat really wanted the Victorian era Clara seen in "The Snowmen" to be the proper traveling companion, and that the BBC forced a modern day Clara on him.
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If true, it really shows on how lovely Moffat writes Clara in that time period. Taken as a trilogy, "The Snowmen", "The Crimson Horror", and "Deep Breath" show her at her absolute most real. Here's hoping that her time with Capaldi in the Tardis allows that sincerity and power to finally get her to where she needs to be.
It was nice to see the Clockwork Men from "The Girl in the Fireplace" return as villains (Side note: Justin Richards' Ninth Doctor novel The Clockwise Man is another great entry for these monsters). Unique among all the monsters introduced since 2005 they actually got creepier and deeper. It was a well done scare, but...
There's this new thing that is going on in the last couple of seasons. The Doctor keeps not quite remembering old foes. When you tie it into the fact that much of "Deep Breath" felt like "Time of the Doctor Part 2" then you see that the real problem is that Moffat can no longer decide who he's writing for.
I believe he's trying to write for everyone. He wants to please old fans and new fans and people just now tuning in. So he makes a Tom Baker scarf joke, throws in a pointed dig at the Tennant fan girls, adds the old joke about redecorating, and even has Matt Smith back for a minute to say a lovely, but pointless goodbye (It's nothing compared to his final words in 2013). He's trying to tease us that the mysterious Missy is either The Master (Missy = Mistress) or the Rani (She used a tyrannosaur back in the day) returned, but is really just wallowing in his own clever misdirection.
The fandom of the show has grown to heights no one can understand, and in doing so it's become a little hamstrung trying to decide where it wants to go. The answer is the same it's always been.
The glory of Doctor Who is that it is supposed to be able to drop you in almost at any point and have you. You can stream "Pyramids of Mars" or "Gridlock" or even "Day of the Doctor" and be right at home. Too many episodes lately feel more like traditional season arc writing, and that is bad news for a show that has almost always defied that approach.
Let's see if it's gets better once Twelve and Clara head into darkness.