Well, this is a surprise. An episode that passed the Bechdel test, multiple times!
And not in an accidental, questionable kind of way. There were several long scenes that only have two characters, both of whom were female. Clara and the little girl talked about their fears, about their pasts, about what they could do to save everyone, with nary a reference to the Doctor in sight. They connected because Clara is a compassionate person who wants to help, not because they were thrown together by the Doctor, or necessity, or anything of the like. The story of the episode came about because Clara became separated from the Doctor, set out on her own, met people and figured out what was going on. I can't remember the last time something like that happened (at least, when the companion wasn't then blamed for messing things up).
We also saw scenes where Clara talked to her mother, and that relationship played a key role in the plot. An episode of Doctor Who with three female characters who talk to each other, without their conversations focussing on the Doctor? Where these characters, even the little girl, have layers and motivations and complexity? Where their conversations, thoughts and relationships drive most of the plot? I didn't think it was possible any more.
The Doctor, however, continues to be incredibly creepy. In the one day he waits for Clara, he goes back in time to stalk her entire life, from the meeting of her parents onwards. Although this contributed to Clara's backstory, and so actually helped to make her a more dynamic character, it once again made the Doctor seem unhealthily, creepily obsessed with her. If it becomes a romance, we're almost getting into Twilight territory.
Luckily, the story does (sort of) address what the Doctor is doing. Too often these days, the Doctor gets away with anything without comment, but here at least, Clara got to say that following her through time, and expecting her to be anything more than herself, is unacceptable.
And this might be why Clara already seems a more likeable and compelling companion than Amy and River Song. Although there's the spectre of her "mystery" in the background, she has depth in her own character, a history, clear motivations for her actions, emotions and relationships that make sense, and the ability to assert herself without it simply being Moffat's sassy kind of "strong female character." Of course, I probably thought those things about Amy and River when they first appeared... but for now, I'm going to take this as a very good sign!