These evil people are clearly suspicious. They have hacked a young woman's head so she can actually understand the internet. #drwho #ew
The current Doctor Who series has exactly zero women writers. Perhaps this is why it's kicked off with a show that fails the Bechdel Test - at least between adults. The child and the nanny do have a brief conversation.
The show has two strong female characters and two strong male characters as well as two additional supporting male roles. The major male players are of course, The Doctor and a character that one might not expect to have a gender: The Great Intelligence. The other male roles are two subordinates at an evil company that hacks people. The strong female roles are Clara, the Doctor's new sidekick; and the woman in charge of the evil company.
As Laurie Penny notes, the evil company adds computer knowledge to Clara's head. Previously, she was entirely inept at getting online, ringing a helpline for aid logging in to wifi. She seems to be a middle class woman in her 20's in modern-day London, who has access to a netbook and a reason to want to get online. The idea that she would be unable to manage something as simple as loggin in to wifi actually seems profoundly unlikely.
Her job is working as a nanny, a reprise of the job of her previous incarnation. The Doctor keeps trying to ask how somebody as obviously clever as herself got stuck as a nanny - an often female-specific job. Things are not getting off to a great start.
The other strong woman character never speaks to Clara. She mostly speaks to her two male assistants, to the Great Intelligence and to the Doctor. At the end, after the Doctor saves the day, she is reset to her state before the Great Intelligence started shaping her personality and actions, or 'whispering in her ear' as she puts it. UNIT finds her sitting on the floor, speaking in the voice of a little girl, asking where her mummy and daddy have gone. Her talents and even her entire self is thus not her own, but belonged to the male Great Intelligence.
Clara did get to save the day in her debut, but only by offing herself in the process. She manages to live through this episode - sort of. She dies twice, but the Doctor brings her back both times. As she's dead, she's especially helpless as a captive and thus is not able to play an active part in her own rescue. However, she's not useless. She discovers the location of the bad guys through a clever insight into social engineering - that the weak point in computer security is usually the people. However, this insight is not entirely her own. All of her computer knowledge and therefore all of her hacking skills, remember, have come from the bad guys. Again, this mirrors her first episode where she also has superior hacking skills than the Doctor, but only because the Daleks have tampered with her mind and body.
The power of women in the episode is, therefore, largely not really their own, but given to them by the machinations of a male intelligence. Meanwhile, the Doctor's abilities come from his own great intelligence and from his magical powers - he uses the sonic screwdriver to 'hack.' This device functions more or less as a magic wand in recent years. In this episode, he also has a magical flying motorcycle. (The linked article at the top mentions JK Rowling as a sci-fi author. I would normally strongly contest this claim, but her influence on Doctor Who is very clear, thus pulling the show further and further away form sci-fi and towards fantasy.) The source of the Great Intelligence's power is not yet revealed in it's current arc - it's a nemesis from the old days, so a backstory does exist, but without benefit of that knowledge, one does assume it is intelligent and powerful in it's own right.
The episode does not contain any great moral questions of good and evil and does not intentionally engage gender roles in 21st century Britain. Instead, it gives us the doctor acting silly, doing magic and centres mostly on London geography. The tallest new building in the capital, which is also a a ticketed tourist attraction, is the main point of action, but there's also South Bank and a joke about the blue police box at Earl's Court.
For those of us who miss Davies, there are not LGBT characters, but there are some POC and there are women working in tech jobs at the evil company, although these are not speaking parts. These women, like their male colleagues, also have gotten all their job training via evil mind control, so this doesn't really imply anything about their abilities, but it's better than nothing, I guess.