This episode was really mediocre. Bill herself is an okay character, and she and the Doctor make a good team, as does Nardole. Unfortunately the plot of this episode just wasn't that great. So, the alien puddle just kept following Bill because it thought it was supposed to, and that's it. Throw in the Contractual Obligation of the Daleks, and that's more or less the episode. The episode is also very derivative of others gone by. The whole thing about the puddle latching onto Heather because of her desire to leave is basically the reason why the people in The Lodger were attacked, Puddle-Heather is reminiscent of the Flood-infected people from Waters of Mars. We had the whole repeating dialogue thing lifted straight out of Midnight. Probably some other things I'm forgetting at the moment.
While I am glad and thankful for the lack of monologues, I have to say, it still takes Moffat way too damn long to get to the point. It was very obvious to me right away the mystery of the puddle reflections is that they weren't mirror-reversed. But of course it was milked out with Heather pointing out the oddity, Bill missing it completely, eventually getting the Doctor involved who has to investigate things for a few minutes before finally providing a lengthy explanation. The Moff could use some work on subtlety too. Was it really necessary to constantly cut to the photos of River and Susan as often as they did?
So, I'm guessing that for this season anyway the university is going to be sort of the Doctor's base or home on Earth, kind of like UNIT HQ in the Pertwee era, only this time we also got the mysterious vault beneath the university which I'm guessing will eventually be an important plot point. Random observation, does the bolt falling off Nardole mean he's in a robotic body? I guess that makes as much sense as anything.
Not a bad episode, but there's quite a bit room for improvement.