Well, it's clear that this year's Doctor Who is going to be all about hints and mysteries. "Day of the Moon" answered some questions, but posed a lot more.
There is certainly a strong suggestion that the Girl in the Spacesuit -- and why did the Doctor decide it wasn't worth chasing after her? I hope this is deliberate, rather than choppy writing, as it was the only duff note in an otherwise strong episode -- is Amy's daughter, if indeed Amy is pregnant, which seems to be uncertain at this stage. The ending of the episode also suggests that the Girl is a Time Lord (!) or at least has a "time head". So, are we to believe that Amy's pregnancy is complicated by the energies of time travel, resulting in a quantum baby and a child with the power to regenerate? Who knows what's going on there.
At one point, Amy refers to Rory "dropping out of the sky" just one episode after River Song uses the exact same words to describe the Doctor. This is probably only to allow Rory to have his comedy misunderstanding regarding Amy's affections, but it's still interesting. Regarding Rory, we had something of an answer this episode to the question of whether he's still an Auton; he certainly remembers his two thousand year vigil outside the Pandorica, which suggests that the Big Cosmic Reset of the previous series did not return him to a fleshy existence.
River seems to have misjudged her relationship with the Doctor, thinking that he should have been intimate with her in his past, when this does not seem to be the case; we might need a flowchart to work this one out.
(On a not-unrelated note, I think I've figured out how River knows the Doctor's secret in "Forest of the Dead"; there's been all sorts of outlandish and elaborate speculation on this point ever since the episode was shown, but I think it may not only be very simple, but also right there in that episode, and it's been overlooked such is its simplicity.)
Speculation will focus on the end of the episode, and the Girl's display of Time Lord abilities, but the most tantalising tidbit for me was the unexpected appearance of a one-eyed woman peering at Amy through what seemed to be some kind of window in reality, and referring to her in the manner of a scientist or doctor. Why is Amy being observed my multidimensional cyclopes, and why do they refer to her as "dreaming"?
My big hope is that Steven Moffat and his writers don't fall into the Lost/X-Files trap and start stringing these mysteries out without a clear plan; from what we've seen from him before, Moffat knows what he's doing, but it's a worry. Still, it was a fun episode, setting up lots of mystery for the coming series, and we've got pirates next!