Broadly speaking I really liked the episode - probably, besides the 25th anniversary, my favourite episode since Asylum of the Daleks. I adore Matt Smith, but I felt like it was the right time to switch up the Doctor. And Capaldi is definitely a breath of fresh air (but it'll be a long time before I stop seeing Malcolm Tucker).
I think the episode really benefitted from the 80 minute format. In series 7 the stories all felt very rushed - there was never any time for the episode to breath or hit genuine emotional beats. The pacing here was a big improvement (although I could have done with way less Paternoster Gang and moping Clara). Everything with the Doctor was fantastic. I especially loved his post-tardis-crash confusion, the restaurant scene, and his speech in the mall.
In terms of Clara, I'm glad they've finally given her a flaw/ characterization beyond perfect-feisty-but nice girl. That being said, her new "control freak" side came across as kind of off-putting rather than relatable. I cringed a bit in the (flashback? Hallucination?) scene where she was screaming at the students. I really hope that's not the kind of teacher she's supposed to be. The frustrating thing with Clara is that Jenna Coleman clearly has charisma and acting chops, but the script never let's her be a real person. She has zero quirks and very little sense of humour. I guess she's supposed to be the straight-man to the zany Doctor, but they've never used that dynamic successfully.
The whole "boyfriend" thing also bothered me a lot because it retroactively made the Eleven/Clara relationship explicitly romantic. The flirty couple-y vibe was one of my least favourite things about series 7, and I was hoping I could just pretend it never happened. But of course, in assuring the audience that twelve/Clara wouldn't be a thing (because "ick, twelve is so old") they had to make mention of eleven/Clara's looove for each other at every opportunity. And also in a way that was really patronizing to the show's female lead.
But, despite these problems, I did actually think the episode was well done. The call backs to girl in the fireplace, fires of Pompeii, and the Doctor missing Amy's long legs were all pretty fun. I didn't see Missy as a River rip off because I'm pretty sure she's meant to be a villain. There are definitely still some rough edges, but I'm excited to see more of Capaldi and I have a good feeling about the rest of the series.
