I turned to my husband halfway through "Deep Breath" and said "I feel bad if this is the first episode for anyone!"
He laughed and agreed, "yes, this is definitely not an introductory episode."
Indeed, it shares in many ways more parallels with Tennant's debut in "The Christmas Invasion" than Smith's in "The Eleventh Hour." Which makes a good deal of sense, as Clara, like Rose, is a seasoned companion suddenly adjusting to the most unexpected change of all. We audiences are expected to be seasoned watchers of Doctor Who adjusting to a new Doctor. Which makes a good deal of sense - Matt Smith was the Doctor who captured the now humongous American audience... and kept their hearts and imagination for three years. Capaldi has the burden of keeping them, a harder role than Smith had as he was being introduced to the British audience which understood the long tradition of regeneration. Much of the younger American audience is going through their first change and it's a big one.
This is, of course, why the last fifteen minutes of the episode are so brilliant. To have the old Doctor literally phone up Clara (and thus, us) and beg her to give the new Doctor a chance - to help him - it is a needed and smart scene to do and provides the most heart-wrenching moments of the episode. No surprise, perhaps, that it is then that Capaldi steps out of the crazed reorientation phrase and shows a softer side, the side that really wins us over to him.
It is a good thing that the episode ended on that note, because otherwise I was not tremendously enthralled by it. The post-regeneration episodes are always difficult. A new actor finding their way into a very iconic role, going a bit too crazy and perhaps not in quite the way they later discover that really works for them. They're adjusting to a new body, we're adjusting to a new face and personality, and the companion is thrown for a loop (whether a regeneration loop or a timey-wimey loop). "The Eleventh Hour" remains the strongest introduction episode for a new actor and indeed for a new viewer (which is probably why it works).
"Deep Breath" is definitely paying homage to penny dreadfuls and other Victorian Horror. Strax remained beautiful comic relief but Jenny was a bit too whiny this time around (although she has good points! why IS she the maid at home?). Madame Vastra is not at her most engaging, but always remains entertaining as comic relief.
It is always a special treat for the fans when the history of the show is alluded to. I, for one, had really thought that we were not going to see an allusion to "The Girl in the Fireplace" again. What a fun surprise to have it as a running joke here! (Nice to reuse another Moffat monster besides the Weeping Angels).
We are left with a lot of questions, as can be expected. Did the Doctor kill the robot, or did the robot jump? Who is the mysterious woman in the mysterious garden and why does she call the Doctor her boyfriend? Is she the woman in the shop who wants the Doctor and Clara to stick together?