I'd say that this episode has a bit of everything: scary aliens, a plot which requires you to think about it (and holds up when you do), and sympathetic characters. I've been aware of Steven Moffat's writing since Press Gang, and I think he's quite talented.
Granted, we didn't see much of the Doctor, but that doesn't really bother me; looking at comics like The Sandman and Lucifer, there were several issues where the lead character either had a small role or didn't appear at all. As a fringe benefit, this also means that we get less of Martha "slaughterhouse" Jones. This episode reminded me of last year's Love and Monsters (and to a lesser extent the Torchwood episode Random Shoes), by focussing on ordinary people. In the case of "Love and Monsters", I liked the way that the characters were able to develop friendships and hobbies beyond their interest in aliens (i.e. they weren't stereotypical geeks), and there was something similar here, since Laurence was more than just "a loser who spends all his time on the internet".
Regarding the main plot, the letter from the past did remind me of the Back to the Future films (Doc Brown's letter to Marty), but I can live with that. Unlike BTTF, there was no attempt to rescue the people who got sent back to the past, so I'm glad that they turned out to have happy lives there. Actually, considering that Doctor Who episodes tend to rack up quite a high deathcount in the supporting cast (e.g. most of the crew dying in "42"), everyone got off quite lightly here. Still, the aliens did come across as quite scary, and I really thought that Laurence was doomed when he was left alone to face one.
For that matter, when Sally and Laurence were inside the TARDIS, I was quite shocked to see it leaving without them, and I actually said out loud "You bastard!" (referring to the Doctor). Still, it worked out ok, although I wouldn't personally have stood in between the statues like that (blocking their view of each other). Will they now need to be kept in a permanently lit room? I wouldn't like to be the guy who replaces that light bulb...
Regarding the statues, the idea that they can only move when nobody's looking at them reminded me of a children's game. I was originally going to say "musical statues" (because of the name), but it's actually more like "grandmother's footsteps". I also thought of the animated series Gargoyles, where the characters were "stone by day, warriors by night!" (Mind you, I recently heard that technically statues of gargoyles have to have waterspouts, otherwise they're grotesques.) However, I don't think that every statue on earth is supposed to be one of that species; I'm just interpreting that as an indication that there are still plenty of potential threats out there.
On a more personal note, I remember watching a TV series when I was quite young which involved statues of dinosaurs which came to life at night; that is to say, they could move, but they were still made of stone. These statues normally stayed in a playground, so one episode involved a young boy who'd been crawling around inside one at the point where it came to life! I think that this series was "The Enchanted Castle" (a BBC series from 1979, based on an E Nesbit novel), but I'm not certain about that. Anyway, I think that helped me with the creepy aspect of statues that start moving around.
Edit: More generally, one thing I must praise about the Doctor Who relaunch is that it's actually popular, particularly with youngsters. I've been out on SJA duties, talking to Badgers/Cadets who watch every episode, so it's no longer just something for SF fans. If the same series can appeal to 40 year old men and to teenage girls, I'd say that it's got to be doing something right. Anyway, here are a few quotes from kids which amused me:
* "Martha is good at killing people."
* "Torchwood is rude."
* [Regarding The Sarah Jane Adventures] "It should be The Sarah Jane Adventure, singular, because there's only been one of them."