The Doctor, Amy and Rory visit modern-day New York. The Doctor has found a nice trashy detective novel about one "Melody Malone" in his jacket pocket, and Amy teases him about how he's obviously started to fancy the lead Femme Fatale. The Doctor rips the last page, claiming that he hates endings. While they banter, Rory wanders off to get coffee and, in the grand tradition of Doctor Who companions wandering off, gets himself into trouble immediately. He encounters a Weeping Angel and is zapped back to Film Noir-era New York, where he runs into an extremely surprised Professor River Song, who's investigating the angels while posing as a private detective.The Doctor starts to properly panic when his novel suddenly starts describing exactly that. He puts two and two together and realises that Melody Malone is Melody Pond, and that Rory's in a whole lot of trouble. By the time he and Amy have managed to land the TARDIS near River (after an initial failure caused by heavy time distortions in that spacetime region), Amy has already read ahead just a bit too far in the book, and there are far too many mentions of deaths, and endings, and goodbyes. The Doctor tells her to stop reading, but they do need to comply with what's already been read. River, who hasn't even written the book yet, finds herself forced to break her own hand. She and the Doctor engage in The Masochism Tango for a while, and both try very hard to be what they think the other wants them to be. River tries to hide her broken wrist so as not to scare him off and remind him that his loved ones can break, the Doctor gets extremely sad that she lied to him and uses some regeneration energy to heal her wrist, and she slaps him hard in the face for his senseless waste of regeneration energy and tells him it's so, so hard to love an ageless god with the face of a twelve-year-old who can't cope with the idea of change. It's also revealed that River was eventually pardoned from Stormcage when the man she killed turned out to have never existed — the Doctor has been systematically removing himself from every database in the universe.Meanwhile, Rory has been zapped around again by a nest of Weeping Angels, but this time just spatially. The rest of the group catches up with him, and they find the Angels' harvesting grounds: a place where people who are zapped back in time are forced to live out the rest of their lives, to be fed on by the Angels forever. Rory arrives just in time to watch his withered old self die, saying goodbye to a heartbroken Amy one final time. Really, properly scared for the first time in millennia, he escapes to the roof, where the Statue of freaking Liberty is waiting to feed on him. Rory decides to kill himself to create a paradox, poisoning the Angels' temporal energy and preventing his future death from happening in the first place. (He also reasons that he may even survive — he usually does.) After a very emotional exchange, Amy decides that she can't live without him. Rory and Amy jump off of the building's roof, clinging to each other. With that, the harvesting grounds never existed, the Statue of Liberty never moved about New York, and Rory never died of old age in that small room.They actually do survive, and end up in the graveyard where the story started, although the web of time is stretched to the point where the TARDIS should really stay out of Manhattan for the rest of her life. However, Rory notices his name on a gravestone right before a surviving Weeping Angel zaps him back in time again. Amy decides that the very small possibility of a life with Rory is better than a secure life without him, and despite the Doctor begging her to stay, she turns away from the Weeping Angel and lets herself be dragged back in time as well. Her name appears below Rory's on the gravestone, both having lived a full life together and died of old age.River knows she must visit her parents with her vortex manipulator one last time to complete the Stable Time Loop, and sets about writing her novel to have Amy publish it. She decides to travel with the Doctor from now on, although not forever, and not always, because "one psychopath per TARDIS" is enough. River then tells the Doctor that she'll tell Amy to write an afterword for the Doctor, and the Doctor remembers about the last page of the novel he ripped apart right at the start of the episode. He then proceeds to race back to the park and reads the page that contains Amy's last words:
Afterword, by Amelia Williams. Hello, old friend. And here we are, you and me, on the last page. By the time you read these words, Rory and I will be long gone. So know that we lived well and were very happy. And, above all else know that we will love you always. Sometimes I do worry about you, though. I think, once we're gone, you won't be coming back for a while, and you might be alone, which you should never be. Don't be alone, Doctor.
Asshole Victim: Grayle chains an Angel and cuts up its face just to see if it can feel pain... causing its screams to attract the other Angels, who stalk him in revenge. He also has Rory dumped in the basement with a number of Angels and only a matchbook to keep them at bay, seemingly just for the evulz. And also turns off the light so the chained Angel can grab River's wrist.
Attack of the 50-Foot Whatever: The Statue of Liberty Weeping Angel. Oddly, since the angels use stealth as their greatest strength, it isn't as threatening compared to the other angels and is just background. It's also portrayed a lot smaller than the real thing.
Better to Die than Be Killed: When confronted by old Rory dying in front of him and the realisation that he'd spend half a century without Amy and trapped as food for the Angels, Rory says to hell with that and decides to jump from the roof instead, creating a Angel-destroying paradox and preventing any of it from happening in the first place.
Big Applesauce: Takes place in New York City, even though the Angels' plan could have worked in any city with lots of people and statues.
Bittersweet Ending: In the end, Amy and Rory are sent to the past with the Doctor being utterly powerless to save them. However, they still get to live out a full and happy life together and Amy leaves a message of hope to the Doctor in the end. But, as shown in "The Great Detective", this didn't help much...
Book Ends: The episode ends with young Amelia still waiting in her garden for the Doctor after he disappeared near the beginning of The Eleventh Hour.
Diabolus ex Machina/Hope Spot/Mood Whiplash: The Angels are defeated and the Doctor, Amy and Rory are free to go on to many more adventures. If only Rory's attention hadn't been distracted for that crucial second by his own gravestone.
I Cannot Self-Terminate: Rory asks Amy to push him off the roof because he can't quite bring himself to jump. She comes up with a different solution.
I Die Free: Rory decides to jump, both because it'll poison the Angels' food supply, and because he'd rather die on his own terms than spend decades stuck in a hotel room all on his own.
Informed Deformity: Making jokes about Amy's supposed wrinkles doesn't really work when you show close-ups of Karen Gillan's smooth baby-face a few seconds later. It also doesn't help that while the character is supposed to have aged a decade since she first boarded the TARDIS, the actress has aged only 2 1/2 years and was only 21 when she first joined the show.
Karmic Death: Grayle, the mobster who captured and tortured an Angel in order to study it, is last seen surrounded by them.
However, while they're technically dead, Amy and Rory lived a full life in the past, and Amy's final note assures the Doctor that they lived Happily Ever After there.
Life Will Kill You: The Doctor cannot prevent Amy and Rory's death in the end... because they lived out their lives in a past that the Doctor could not reach. It was something the Doctor was always going to have to face; the anguish comes from having to face it much sooner than he had wanted.
Like an Old Married Couple: The Doctor and River have their moments. For instance, the Doctor says he started reading the book because he liked the cover. When he shows it to River, she says she hates it.
The Maiden Name Debate: Rory's room in the hotel has 'R. Williams' outside the door. Rory and Amy's tombstone has them both as 'Williams'. In the Afterword, Amy also refers to herself as Amelia Williams.
Oh Crap: River's wrist is trapped in a Weeping Angel's hand. The Doctor is about to break her wrist to get her free, because it was written in the book when Amy skipped ahead, then changes his mind and tells her to get free without breaking any bones. Cut to a bit later, it seems like she's somehow managed just that... and then the Doctor grabs her hand to run off and she cries out in pain.
There are also several courtesy of the book. Most notably when the Doctor reads that Rory was suddenly in the story after leaving to get coffees, and when he sees the final chapter is titled "Amelia's Last Farewell".
They all get one when River notices that one of the angels is smiling, and it then escalates when they look into Rory's room, and realise just how screwed they are.
Sealed Room in the Middle of Nowhere: The "Battery Farm" set up by the Angels. By creating a motel and then sending their victims there, they can keep feasting on the life energy of their victims, hurtling them back in time and proceeding to keeping them locked for decades just to create a Stable Time Loop in order to ensure the events happen.
Amy and Rory jumping off a building to commit suicide? Steven Moffat's Sherlock did it earlier that year.
The name of the first chapter in the book is "The Dying Detective", which is also the name of an original Sherlock Holmes story.
The Statue of Liberty being an Angel may be a reference to an April Fools' Day gag pulled by The SCP Foundation, where established SCP 173, another murderous statue that can only move when not observed, was changed into the Statue of Liberty.
The Doctor and Amy visit 221BC China to leave a message for Rory and River.
Temporal Paradox: Deliberately breaking one of the time-loops the Angels create will poison all the other loops in the vicinity - of which there are plenty. Unfortunately, one can only do this so many times, and when Rory gets caught after the fact, that timeframe cannot handle another paradox.
Tempting Fate: Rory stops to look at the gravestones instead of getting in the TARDIS and running like the Doctor told him he'd have to.
Thanatos Gambit: Rory jumps off the roof of the building to kill himself twice in the same night and create a paradox that will destroy the Angels.
They Killed Kenny Again: Rory brings up his own Kenny status in the run-up to jumping off a roof (which he hopes will be undone via paradox) after seeing his future self die in bed. Who else could pull that off?
Amy: You think you'll just come back to life?
Rory: When don't I?
This episode marks Rory's seventh, eighth, and ninth deaths of the series. Which ties him with the Doctor, whose second incarnation didn't die, but was forcibly regenerated by the Time Lords.
You Called Me X, It Must Be Serious: When Amy is considering whether or not to let the angel send her back so she can be with Rory, the Doctor calls Amy 'Amelia' and River calls her 'Mother'. Amy, in turn, calls them 'Raggedy Man' and 'Melody'.