WARNING! THERE MAY BE UNMARKED SPOILERS!
Amy and Rory went on to make friends with Billy Shipton from "Blink"
Both were sent back by angels, both got involved in publishing. It was noticing that they all shared a dislike for statues that brought them together.The reason there's no record in history of the Statue of Liberty walking over to Battery Park...
The paradox erased all that just like it did the angels themselves.Amy and Rory from any point after this episode are Time-locked for the Doctor
As a result of having been the center of so many paradoxes (Amy's changed her past before in The Girl Who Waited for example), Amy and Rory essentially became Time-Locked with that last Angels action. The Doctor can sense time fluctuations to some extent he knew that he wouldn't be able to go back for them. Additionally, the reason it was fixed when written is not because it was written in the book, but because it was written by River, who was directly involved with the incident. Changing your own personal history is always a risky idea.The Doctor can't see Rory and Amy again because of reincarnation.
When Rory and Amy died in the past, they were reincarnated into two teenage children living in Oregon. The Doctor can't interfere with Rory and Amy's timeline, or doing so would prevent the reincarnated versions from existing.Brian will never know about what happened to Amy and Rory
As a way of tying up loose ends, one Angel made its way to Brian's home. It successfully zapped him out of time, and he lived out the rest of his life as Father Brown.- Jossed: There's a YouTube short released by BBC called PS[1]
which shows that Rory and Amy's adopted son, Anthony Brian Williams, arrives to Brian about a week after they left at the end of The Power of Three with a letter from the two explaining to him what happened. It was storyboarded and they wanted to shoot it, but they couldn't get the actor for Brian due to a scheduling conflict, so they released it with narration from Arthur Darvill.
The lone angel isn't a Karma Houdini
We don't see The Doctor and River enter the TARDIS after Amy is zapped into the past, we cut to them already inside. We don't see what they did to that Angel because it was too horrific for us to see.