The Impossible Astronaut has made a splash with great ratings, audience share and AI, not to mention generally favourable reviews and Matt's wholly deserved BAFTA nomination. There seems to be some confusion as to what the plot actually was that I find rather baffling to be honest. I think that Who fans and TV fans in general have become accustomed to one episode storylines. In general even Who's two parters tend to comprise of episodes with their own individual beginning, middle and end. Hence they all (bar the End of Time) have individual episode titles.
This is a relatively new innovation for Doctor Who. For 26 years the TV show merrily spent three, four, 6 or more weeks developing the storyline. Can you really tell for instance what the plot of the say the Dalek Masterplan, Evil of the Daleks or the Curse of Fenric is or will be from part 1. By the time you get to the '90s and the New and Missing Adventures you have story's in which the plot is kept deliberately obtuse or non-linear simply to prevent the boredom of fans who already know the standard tropes and storylines.
Seen this way it should be appreciate that the episode is perhaps rather less confusing than some have suggested. Indeed it is not hard to state the plot:
1) Weird aliens (The Silence) have been on the Earth for a long time. They have built a massive network of underground tunnels using the "other" TARDIS. Nobody on Earth knows about this because The Silence have the ability to make sure that people forget them instantly.
2) The Doctor knows about The Silence. His future self has spent a couple of centuries running from something related to them (probably the knowledge of his own impending death) but he has now decided to face up to this.
3) Future Doctor calls Amy, River and Rory to a meeting to give them the information to get current doctor to America in 1969 (and probably to witness his own death, thereby hoping to retcon it). Future Doctor then dies.
All of this would be "Part 1" under the old 4 episode stories. Its basically setting the scene, but not actually moving the plot along much. Compare with, for instance, Planet of the Daleks wherein 25 minutes are spent wandering aimlessly around a jungle only to find (gasp) a Dalek*. We don't necessarily know the "Why" for a lot of the Future Doctor's actions, but we don't actually need to at this stage. It's not a plot hole, its a point to be developed later in the story.
4) Current Doctor goes to America as instructed and starts to investigate the silence.
5) Amy shoots what she thinks is the Astronaut who killed Future Doctor.
That is episode 2 of the old style structure of story. Nothing complex about that at all.
One review I read made the point that the episode felt very much like the first part of a season finale and that may well prove to be the most astute observation as the indications are that season 6 will be at least as intense and intricate as season 3 was. Looking back, The Impossible Astronaut matches the approach of The Pandorica Opens far more than The Eleventh Doctor (or perhaps more fairly Smith and Jones). New Who has generally applied the KISS principal for fear of alienating the general audience and Moffatt is to be commended for attempting a shake up, particularly at the start of the season.