I'm going to split these reviews up into three parts. Things I liked, things I didn't like, and a spoiler section at the end. The first two parts will not contain any major plot spoilers.
Things I liked. The Doctor's office is very nicely decorated. It reminds me of Professor Chronotis' TARDIS in Shada. Plus I love the attention to detail on the set with the photos he keeps. The episode also reminded me a lot of the first proper Clara episode with the same over all tone and feel. And by the first proper Clara episode if you don't know what I mean by that I'm referring to the first time we actually see the real Clara rather than her copies. I like that this episode kind of sets up the over arching plot for this series. I really want to know what's inside that vault. There isn't really any information on it at this point. I also love the camera work and editing in this episode. The way it's shot and how it transitions to different shots along with the dialog is just amazing. It's kinda hard to impress me with something as simple as aiming a camera so that really says a lot that I'm even noticing the way this episode was filmed.
Things I didn't like. The plot of the episode was kind of predictable. I figured out what the monster of the week was trying to do before the characters in the show did. I'm not really liking Bill at this point, though that could change as her character develops more. It's just kind of the worst introduction to a new companion I've ever seen. There's also something that appears in the episode which should be awesome but just seems kind of random and makes no sense.
One of the photo's on the Doctor's desk was a picture of his granddaughter and first companion, Susan Foreman. I'm wandering if they're ever going to bring her back in this series especially considering this is the first time she's ever been directly referenced in the new era of Doctor Who.
When Bill asks "When someone is gone do photos really help" the camera shows his reaction and then shows a close up of the Susan and River photos on his desk. The next scene is Bill for the first time seeing photos of her mother. This is one of the best shot and edited sequences I have ever seen. It adds to the conversation they were having without anyone actually saying a single word. The actors expressions help this as well. I actually stopped to rewatch this sequence about three times before I finished the episode. The whole thing is like that but this one in particular was really great.
About five to ten minutes before they revealed that Heather was trying to get Bill to travel with her, I had already figured that out. She only ever went where Bill did and she did promise to take Bill with her when she left. There was a moment when I think they were trying to get you to think she was going after the Doctor but the whole thing seemed very familiar. Like the entire plot was almost borrowed from a previous episode. It just made it very predictable and boring. I do kinda wish that Heather had been the companion instead of Bill but maybe that's just because of her asymmetrical eyes. I don't know why I just like weird things like that.
As for why I don't like Bill... she says Doctor What instead of Doctor Who, she sees the Doctor reflected in a mirror in photos of her mother immediately after telling the Doctor that her mother died when she was a baby and she doesn't have any photos of her but then never actually confronts him about it, she sees the Doctor and Nardall at that mysterious door and again never questions it, and it takes her a stupidly long time to realize that the TARDIS is bigger on the inside. At first she calls it a kitchen then thinks it's a lift. In the first scene of the episode the Doctor practically brags about how smart she's suppose to be but then we never actually see her do or say anything intelligent. She comes off as a blooming idiot.
Finally that seeming random thing that shows up for no apparent reason. The Doctor gives Nardall a Sonic Screwdriver... but it's a classic Sonic which was destroyed and replaced and is supposedly the same sonic just with a different outer shell that the Doctor is currently using. And there's no reason why he would even need to do that since the Doctor could of used his own Sonic himself. So something which should of been really cool to see return is instead placed in the show for no reason other than hey here's the classic Sonic Screwdriver which shouldn't even exist at this point.
I have no doubt that the series will get better as there's a Multi-Master story coming at some point and I love the Master but we're off to a bit of a shaky start.