I had a lot of problems with this episode. The Doctor doesn't do anything, he doesn't solve any problems except River's wrist, he just gets whiny and angry and scared, he just reacts to the things around him and gets his mind stuck in what he can't do rather than all the possibilities of what he can or could. He doesn't try anything, he just accepts that they're screwed. Of course, Rory barely gives him time to try much of anything before deciding it's go-time.
The idea that writing in a book makes it a fixed moment seems a little constricting, we've seen timeline changes before in this series going back to 9, and it's such an arbitrary thing. We've had Amy Pond most recently turn old and die in front of them without it becoming a fixed thing, yet Rory does it and all of a sudden it's impossible to change, "sorry sport, you're toast, enjoy the next 50 years here". The Doctor not finishing books also seems like a cheap conceit to this story rather than true to his personality.
That actually gets me on another tanget, the Doctor's recent inability to face the state of change in the universe, all of a sudden he's incapable of letting go of things precious. The Doctor has had children and grandchildren come and go, the Doctor has watched companions age and move on and die and survive without him, but all of a sudden in the last season he's gotten incredibly immature about such things to the point where it's a driving force in this episode and it rings incredibly false.
Rory and Amy's leaving was such a cheap-out. For this season we've been watching them grow closer to wanting a real life, to struggling with the idea of living the lives they had against travelling with the Doctor, and they were nearly ready to give it up last episode until at the last second they didn't. Here, they're back to where they were last season except not really obviously since this is "it". And what a cheap out it was, too, like Radar bursting in and letting us know that Col. Blake's plane was hit and spun in. What happened with wanting to have a normal life? And why would Weeping Angels from the past magically appear right where they need to in the present to zap Rory? Wasn't their plan to zap them to the hotel? That's gone now, it never even happened, so this is a random Weeping Angel. The ending also smacks of a copy of what happened to Rose Tyler - beloved companions are forced by circumstance to go somewhere that the Doctor cannot ever follow.
River shows up out of the blue, it's a fun surprise but it has no substance, there's no reason for her appearance there, so she's just there because the shoddy script says she should be. The episode introduces us to 3 characters - the detective, the crime lord, and the thug - and none of them get any time to be anybody, they're just cardboard characters there to set the plot in motion and then disappear. The crime lord is given a token piece of character-business but it goes nowhere. Then they all disappear, leaving just our heroes and some statues. I'm also disappointed lately in how little action the TARDIS gets, under Moffat lately it's become a mere one-room conveyance and nothing more, there's barely a thought given to the fact that it was challenging for the TARDIS as well.
The weeping angels also really are on my last nerve now, they've become peek-a-boo zombies, all they really are are monsters playing 'red light, green light' to little effect. In Blink they were horrifying, yet every instance since has taken away more and more of what makest hem unique. What was the point of the giant statue of liberty? That should have been something awe-inspiring yet instead it is just a backdrop, it just walks up, looks scary, and threatens nothing - towards the end it doesn't even obey the angels' rules, as no characters are looking at it yet it still just stands there enthralled by Rory and Amy having a soap opera moment. There's also not enough thought put into the torturing of a captured angel, shouldn't something like that resonate with the storyline, or at least piss off the Doctor who hates stuff like that even when it's done to his enemies? Instead it gets a grimmace and a vengance ending and is forgotten.
Revisiting early 20th century Manhattan didn't really use the city well, there was a street, a bridge, the crime lord's house, and the hotel, but almost nothing about being in the 1930s or in New York mattered to the story at all. Streets and buildings were empty, there wasn't much period-specific activity, and once we were back in time there wasn't that New York flavor, so why were we there? This felt like yet another dropped intention to do something more.
So what does work here? Aside from a no-parking sign they should have removed, the 1930s setting looks good and is fun to play with. The real Manhattan looks great and adds flavor to a Doctor romp. The acting was full tilt, even if they did pair off characters too often.