River asks the weird old man why he's even there, and he produces his own blue invite. They all trip out on that, and he introduces himself. "I won't be seeing you again, but you'll be seeing me," he says, and River notices that the invites were numbered. Then, if you're American, there's a commercial break for no real reason at all, in the middle of her sentence. When we come back they discuss that: Who got Invite #1?
Instead of discussing this, mostly Amy tells everybody to shut up a whole lot, and Rory goes on and on about "space 1969," and they slowly realize that our Doctor, Doctor 909, is the first invitee. They come to this conclusion when he appears out of nowhere in a diner, holding his invitation. Everybody yells at him for inviting them to his murder, and he gets slapped about the face a whole bunch and generally yelled at, but he's remarkably buoyant about all this. They realize they can't tell him that he got killed, because there are bigger plans going on here than whatever they've possibly spotted yet.
For personal reasons, River's sad to learn that a lot of the shared things in 1103's diaries -- their overlap -- are back to having not happened. (In the movie, River will be played by Rachel McAdams.) They go back over the facts one more time from ten seconds ago: "We've been recruited. Something to do with space, 1969, and a man called Canton Everett Delaware III."
Recruited by who? Obvs. the Doctor, but they can't tell him that because of the end of that story, about which they have a second sidebar without him. They know it's not about revenge, or about saving him from what they saw, so then what? Last time this exact same storyline happened -- two whole episodes ago -- the entire universe blew up, so you can understand their ambivalence.
The Doctor doing cute things is pretty much the main attraction here, so he does some cute stuff, and Amy continues going back over everything that just happened over and over, and River pulls out some kind of fatalistic nonsense that pretends to make sense in the same way that everything River does and says pretends to make sense: "The Doctor's death doesn't frighten me, nor does my own. There's a far worse day coming for me." What do you mean, River? Oh, nothing at this time? Cool.
The very best thing about having a show with zero narrative accountability means you don't have to spend time making things fit together or avoid contradicting themselves: You can just do whatever you want, and then tell us that was how it was supposed to be all along. Just toss any old crazy awesome crap together -- space whales and Elizabeth X and scary face monsters and trapdoors and weird music and water falling in glasses and people wearing masks and time-travel that doesn't even pass a basic bullshit test -- but as long as you've also intercut three random scenes of other stuff happening, at the end of the day you can point to it and be like, "See? Brilliant."