Nearly the first thing they do upon meeting up in the middle of nowhere, after having lunch in a faux American diner in Cardiff, is to have a picnic on the shores of Lake Powell in Utah. Most will remember this as the setting for the Death of the Doctor, but the scene starts by focusing on The Moon, and The Doctor explicitly refers to the Moon.
It's a subtle reference but in Silence in the Library one of the characters is Doctor Moon who tended the little girl. We learned that Doctor Moon was actually a moon-sized computer in orbit with the planet-sized library which was the setting for Silence in the Library. Hence the story title, Day of the Moon, could be referring to Doctor Moon.
And while we're mentioning the title, Silence in the Library, we should recognize the spooky creatures in Impossible Astronaut are supposedly called The Silence (according to The Doctor Who Podcast). All last season we were regaled with the phrase "Silence will Fall" and we still don't know precisely what that meant, but Silence in the Library can be seen as a significant prior use of the word, in Doctor Who.
Anyway.. lets get back to the episode.
The astronaut costume is the next connection to consider. In Silence in the Library the archeological team lead by Professor River Song (this episode was our first time meeting her) was wearing space suits as well. The primary connection I see between them is the opaque nature of the facemask being emphasized.
The strongest connection between the episodes is when Rory and River are breaking into a chamber deep in the catacombs and River is explaining what she meant by not being afraid of her death, or the Doctor's death, but that an even darker day is coming. She then explains how hers and the Doctors timelines are going in opposite order, where every time they meet her experience of him is he knows her less and less, and that she knows a day is coming when she'll meet the Doctor and he will never have met her. She says she believes that meeting will kill her. Of course we've seen their first meeting, it was in The Silence in the Library. And at the end of that first meeting, River Song did die (while saving the Doctor) except that the Doctor had given her a special Sonic Screwdriver which saved enough of her life essence that she could be deposited in the library records computer.
Plausibly the River Song which got deposited in the Library worked out a way to build a Robot to walk around the physical world. She's not the sort to be put to pasture in cozy retirement, is she? She's the sort to die with her boots on in protection of her man, the Doctor. It makes sense that she would want to venture out of the Library's computer and continue that role, eh?
But what would cause her to venture out? Maybe, living in the Library's computer with access to all its data banks she came across information the Doctor must know? Or.. who knows.. The possibilities became hazy in my mind.
If this is indeed the connection this is a story line which will take a season or more to play out. I can't see that being explainable in one episode. Especially considering that in 2013 we have the 50th anniversary and Steven Moffat is most likely setting up a story line which reaches that far into the future, or plausibly that story line already began last season? Perhaps based on story threads he put into episodes he wrote before becoming the show runner?