The problem with THE ANGELS TAKE MANHATTAN is that while it has a number of nice moments, it simply doesn't convince for two reasons:
Firstly, as every reviewer has pointed out including you Friday, why can't the Doctor travel back to 1941 and pick them up? Why can't he tell Amy "I can't go to NYC but travel to Chicago and I'll pick you up there in a couple of weeks"? The mechanics of the time distortions simply aren't clear and it doesn't work so everyone saw that episode then afterwards begain rewriting the resolution scene as either explaining away why the Doctor can't go back or that he could've. When your audience feels compelled to rewrite your story, you've failed, no matter how entertaining it was.
Secondly, it simply doesn't convince emotionally. This would've been a great ending for Sally Sparrow if she'd been the companion. But not for Amy and Rory. They're nothing to do with the Weeping Angels. In THE GOD COMPLEX, the Weeping Angels were in David Walliams' nightmare, not Amy's. Rory, if I recall correctly, has never met them before. But the Silence... the Silence is all about Amy and Rory. It's been even more intertwined since River was revealed as Melody. Then there's the whole theme of "waiting". Rory waited for Amy. Amy waited for the Doctor (twice). They keep waiting. When I heard the Weeping Angels were involved I immediately thought the Angels would use they're "sending people back in time" trick to make the trio wait in some capacity to the point where they've lived their life and that's all that's left. Especially with all the hints of Amy and Rory growing older faster than the Doctor expected. In fact, I expected the Doctor to realise he's kind of been a Weeping Angel; he takes Amy and Rory off on adventures for months, returns them to the time they left. To their parents it'll look like Amy and Rory aged 50 years in 5 years and their lives were stolen. But, that's if you have to use the Weeping Angels. Frankly, I expected the Amy & Rory send off to involve Madam Kovarian and the Silence. Emotionally, it doesn't feel real. It just doesn't thematically fit with the story so far, it feels like the ending for a different companion, quickly truncated. And it has no set up.
There was another, unrelated problem: the Statue of Liberty is a Weeping Angel and doesn't do anything in the story. How is that not the focus of the story? It's such an awesome idea and they did nothing with it. It was wasted here. But there was good stuff, particularly the acting; Matt Smith's utter shock at the sudden loss of Amy was heartbreaking.
But I'm disappointed in this season. My favourite episode was THE POWER OF THREE and it was rather weak. A TOWN CALLED MERCY was CURSE OF THE BLACK PEARL bad. DINOSAURS ON A SPACESHIP was a sort of Douglas Adams kind of fun, though not as good as THE LODGER. ASYLUM OF THE DALEKS I found boring because Daleks are crap (only time I've ever liked them was THE BIG BANG). THE POWER OF THREE was really wonderful until it ended. I actually can't remember how it ended. Really. I remember the build-up and I can't remember the end at all. They find a guy on a spaceship who is a Gallifreyan bogeyman and... something? I actually remember the ends to all the others. Very disappointing. Nothing on the level of THE ELEVENTH HOUR, or the Angels two-parter, or the Pandorica two-parter, the Silence two-parter, THE DOCTOR'S WIFE, A GOOD MAN GOES TO WAR, THE GOD COMPLEX or NIGHT TERRORS. Amy and Rory deserved better for their final send off.
I'm certain Moffat had trouble behind the scenes for these five episodes. He was gearing up for the 50th anniversary and Karen Gillan and/or Arthur Darvill wanted to leave, and he didn't want to set up the 50th anniversary story lines with Amy and Rory as they'd be leaving, so he put it off until the new companion and gave us five stand alone episodes with a slight continuity for Amy and Rory and nothing else tying them together. I dunno really, something wasn't working this time round. Hopefully he'll grab his stride, but I wonder... SHERLOCK is amazing, but he deleted his twitter account and I have a feeling that criticism is no longer anything he pays attention to, and he's starting to not question his work the way he was during the fifth season. We'll see if this is a hiccup in quality due to changes behind the scenes (let's not forget, two associate producers left, under pleasant circumstances though) as opposed to a downward trend.