These will be really quick thoughts since I’ve only watched it once.
My first thought was that it looks like they’re trying to bring a more cinematic quality to the episodes. I saw a lot of tight corridors and dimly lit rooms, implying a few more horror/thriller type episodes. I also noticed open spaces and expansive scenes, making me think there will be a few epic events. The special effects look to have improved over previous series, which I hope doesn’t distract too much from the excellent stories that have defined the show.
The inclusion of the Mistress in the series will be interesting. I haven’t been the biggest fan of the Master, but the Mistress has been different enough that I’m willing to see what she brings to the table. The appearance of Maisie Williams will draw a lot of attention, I’m sure. I don’t watch Game of Thrones, so I know nothing about her acting ability (given how much people love her, though, I’m sure she’s great). I hope they’re not bringing her in simply as a ratings draw, but have a substantial character for her.
The last line of the trailer “I’m the Doctor, and I save people” was an interesting way to end it. There was no context given, but I’m of the opinion that Capaldi’s Doctor is taking off the kid gloves and moving towards letting humans stand on their own. I think he wants to see if humans can really make the choices he’s taken upon himself for centuries (as in “Kill the Moon”). He’s also seemed more willing to sacrifice lives than previous incarnations (as in “Mummy on the Orient Express”). My initial thought is that the Doctor is actually trying to convince himself that that is what he still does (provided the line is actually in an episode and not just for the trailer). I could be way off, but for now that’s my guess.