Before the opening credits we see both Amy and Rory shot (apparently dead), River Song jump out of a skyscraper, and The Doctor as a prisoner in Area 51. Yup. Before the opening credits. What happens from there is a twisty story which took 3 viewings to begin to understand. I recommend taking this show in the appropriate dosage. Several times.
The guy playing Richard Nixon is a total disappointment - he's not believable, and all they use him for is to trot him out to wave is magic Presidential Aura and make some plot point disappear. In Old Who when the Doctor got detained by Security he might spend a whole episode moping in a prison cell trying to cheer up his companion, but in New Who they show him in league with the President magically dissolving resistance away in a puff of smoke.
There are three main places the story covers: a) an abandoned orphanage, b) the warehouse they discovered in the Impossible Astronaut, and c) the control room underneath the warehouse.
It's the Orphanage where the most interesting stuff occurs.. First, it clearly demonstrates how deeply the Silence guys cause people to Forget. The guy who lives there - clearly having a lot of hatred and anger towards the Silence, writing angry messages on the wall but not understanding how the messages got there. And then Amy as she explored, the filming was astounding. They showed her one second without marks, then the next second with dozens of marks, (which we know that's how Amy, Rory and River decided to help themselves remember), and hence we knew Amy had seen dozens of the Silence, had an interaction with them, but we don't know what they said.
And then down the hall there's a room that's just extraordinarily strange. As she approached - a peep hole opened with a woman inside saying something about Amy dreaming, then closing the peephole, and the peephole completely disappearing. Inside the room she finds a little girls place along with some pictures that include one of Amy holding a Baby.
How did Amy come to be holding a Baby? They're implying it's her Baby but of course it could have been any old Baby, but the setting strongly implies it's hers. If so, where did this Baby come from, who's the Father, etc? Presumably the Baby was the little girl in the astronaut costume, and it appears the little girl broke out of the costume and is running around on her own. And finally, it appears the little girl is a Time Lord who is playing around with regenerating herself whenever her body dies.
Given there's only one known Time Lord around it's a pretty foregone conclusion who the father is, eh? Unless, that is, there are other Time Lords who didn't participate in the Time War? That is, there's likely a small number of other Time Lords were not engulfed by the Time War and are instead running around loose. Perhaps one of them were the father but the official story line has been that The Doctor was the only one to escape the Time War.
Over at the Warehouse we learn that the Astronaut costume is a highly advanced life support system, high tech communications, and weapons system. The Silence do appear to be have highly advanced technology hence it's likely they built the costume. The orphanage guy said something about some others who stressed upon him the importance of taking care of the little girl. The Astronaut costume would appear to be part of the plan to take care of the little girl?
In the control room - that was kinda weird. The Doctor sees it, recognizes it as the thingy from The Lodger, and expresses a hope he'll learn why that one had been abandoned and this one was still active. This makes the Lodger seem a more important episode to consider, and I did rewatch it recently but it didn't really enlighten me any about the current episodes (Doctor Who - The Lodger is more significant than you might think). What I said then is doubly true now, at the time it seemed like a nothing filler episode except it had a few significant things woven within it.
We're left with a lot of loose ends flapping in the wind, and a few answers. Such as who the Silence is Thoughts on The Silence (Doctor Who S06).