Honestly, I think this episode could have been just one, and not a two-parter. It didn't have enough to sustain two parts. I was kinda, get on with the story at certain points of both episodes. And beyond the weak storytelling (coming from Moffat, a surprise, I know ... oy, I hope he gets creative juices rejuvenated for when the takes over the show), I really found that I only liked three things ...
1. Donna. As always, Donna rocks. I do love her so. Her alternate universe world broke my heart. When she said "mummy won't close her eyes," I teared up, and that's all thanks to Catherine Tate's acting skills. And, also, she managed to deliver the one tart moment in the entire episode ("I've been dieting!"). Finally, I sniffed when her "perfect man" saw her too late, and, of course, couldn't get her name out. Awwwww.
2. Anita was a good character.
3. Alex Kingston's acting. I really think Alex Kingston is wonderful ...
which brings us to things I didn't like ...
1. Alex Kingston's character. Yes, yes, I understand that Doctor Who DOES NOT revolve around Rose. But when you have episodes bringing her up, the Doctor still affected, a whole long trailer that aired BEFORE these two episodes featuring Rose's story, throwing in some chick who knows the Doctor well enough to know his name, well ... honestly, it pissed me off. I wanted her to die. I wanted her to screw up whatever future she had with the Doctor, because damnit, at this point in the show (because of how they've dragged out the Rose thing), I'm not ready to find out he's that emotionally close with someone else. When we found out that River told him his name, thus he had to tell her, my first thought was: He never told Rose his name, and then I got unreasonably pissed (unreasonable, I admit, but still there none-the-less).
With Moffat taking over, obviously the 'Rose' era that's been prevalent with Russel T. Davies hard-on for the character will be gone ... but couldn't Moffat had waited until AFTER time where Rose WAS so much still a fabric in the tenor and emotion of the Doctor had passed. Like, you know, when HE takes over ... a year and a half from now?!?!?
So, yes, call me a silly shipper, but it bugged me because while I'm fine with the Doctor having his little dalliances, at this stage in the game, it's been set up throroughly that Rose is special. Don't bring this woman out of nowhere and make her the be-all and end-all for the Doctor in two episodes when I had two years to fall in love with the Doctor and Rose.
2. As I stated above there wasn't enough plot to sustain two episodes. And that really is the biggie. It was a good idea, but could (and should) have been condensed into one episode, and should have cut out all of the Doctor/River special stuff. She could have just been a future companion who was special like Martha or Donna or Sarah Jane and the story would have worked just as well.
ETA: Ooh!!! the_spin is awesome. Her write-up of the episode just made all of my pissed-off-ness disappear. She's brilliant. It DID make sense that all of what happened, including the Doctor telling her his name was for THIS situation that happens in the library, because the Doctor would know he needed to be convinced. So I can pretty much believe now that, yes, River was another companion of the Doctor's who was special and who meant something to him (as do all his companions ... he really does love them all in his own way, in different ways), but that doesn't make her as much as or more than Rose. Yes, yes, I know I'm harping on this but I just finished rewatching season one and am rewatching season two, and then I'm probably going to rewatch them both again (ahh!!! the joys of summer reruns!), so I'm on a Rose/Doctor high.
Sadly, I didn't realize until after I was more than half-way through when I just couldn't stop that I really should have waited until AFTER this season was over to restart marathon-in DW what with the looooooooooong break coming up. Ah well, too late now.
Back to this current episode ... with my issues with River Song resolved, unfortunately, I still think it was a weak two-parter. As one episode, I believe it would have been much stronger.
ETA: Man, now I wish I had read the_spin's journal on it first because she made it all work for me. I LOVE YOU!!! I'll still keep my original thoughts up, but add a bit more thanks to her post -- note, it's a friends-locked post, so if you're not on her flist, you can't read it. But I have a brief sum-up above.