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In The Hungry Earth, where Amy, Rory and The Doctor visited a drilling site a couple on the ridge waved to them.
The Doctor says that that's them 10 years in the future. But if Rory and Amy are sent back to the 40's by the Weeping Angel, how could that have happened?
It's the nature of 'Who' that certain interactions can create a specific event that must take place in order for the future to unravel in the correct way. This event is described as a fixed point and can never be changed without massive (and potentially catastrophic) disruption to space and time.
Given that New York already a hot spot for temporal activity, it seems that because the Doctor is unable to rescue them immediately, their presence will have such a substantial effect on the world that removing them later (for example by travelling to another point nearby and travelling in space to their location) will still have a considerable impact.
By comparison, their standing at a great distance and viewing their younger selves doesn't have enough of an effect on the timeline to qualify as a fixed point. The future can be violently altered without affecting the rest of the universe since their presence (or not) doesn't make that much of a difference to the world.
In "The Power of Three" (S07E04, the episode before "The Angels Take Manhattan"), Amy says that she and Rory have been travelling with the Doctor for 10 years.
We think it's been ten years. Not for you, or Earth. But for us. Ten years older, ten years of you. On and off.
(Timestamp 04:24-04:33)
This means that they could have already gone back and waved to their 10-years-younger selves.
Time travel.
The went back and waved to themselves sometime after this episode (probably during their anniversary trip in "The Power of Three", since Amy mentioned in that episode that she and Rory had spent a total of about ten years together in terms of time on Earth + time on the TARDIS by that point, which aligns with the Doctor's estimate of the Amy and Rory on the hill being from ten years in their future, and it fits his comment about them feeling nostalgic), but before the events of "The Angels Take Manhattan".
Shortly thereafter, the Eleventh Doctor arrives in Cwmtaff with Amy Pond and Rory Williams, having promised them a vacation in Rio de Janeiro, missing by several thousand miles; the TARDIS has brought them to the wrong place yet again, much to the annoyance of the companions. As they look across the valley, Amy spots two figures waving at them from the opposite hillside. It is Amy and Rory from ten years in their future, coming back to revisit past glories. Though she finds this "interaction" with her future self thrilling, Amy still wants to go to their intended destination.
The revisiting of "past glories" must have happened in between the events of two episodes. You mustn't forget that sometimes there can be a big gap in between episodes, of which we can only speculate what happened. Also, "The Hungry Earth" is the eighth episode of the fifth series, and "The Angels Take Manhattan" (in which Amy and Rory get sent back in time) is the fifth episode of the seventh series. A lot of time in between, 'ey?
Some people think that it was actually their future selves warning them for something, and not waving at them.
Well, whatever the case, I am sure it has nothing to do with and it doesn't interfere with the unlucky events in "The Angels Take Manhattan".
Besides, their future selves were standing quite far away from their present-day selves, so the distance wouldn't have been enough to create a fixed point in time. Also, they didn't talk to each other, while Amy did say farewell to the Doctor in The Angels Take Manhattan, thus creating a fixed point.
In The Angels Take Manhattan the Doctor had mentioned that Amy was looking older. So perhaps they were having long gaps in between adventures with the Doctor. We don't know specifically when that Amy and Rory were taken from so it could have easily have been after The Hungry Earth time.
In "The Power of Three", S7, Amy tells the Doctor they think they've been travelling with him for ten years of their lives (not ten years of linear time on Earth but ten years of aging in the TARDIS and at home).
So around ten years after "The Hungry Earth" in S5, and around the time of "The Power of Three" in S7, Amy and Rory got nostalgic (as they were also accepting that they'd stop travelling soon) and went back to see themselves, since they remembered doing that.
They would've been in their early 20s when they started travelling with the Doctor, so I don't think it's unreasonable to assume they could've been in their early 30s after years of on-screen and off-screen adventures with him.
