Like many other reviewers, I was interested in this vision of a southern California where the familiar is mingled with desolation. It was fun. I really did like the book overall and for the same reasons given by other reviewers. But I also agree with many of the criticisms.
1) Turtledove talks down to his young readers. Heinlein did not do that. There is too much repetition (as some have pointed out) of arguments, etc. Teenagers want to be treated with respect. Mostly Harry does that. His characters are in difficult situations, usually not of their creation, and they generally come off well. That is, they get by, using their wits and the advantages of their knowledge. Luck plays a part too.
2) No ipods or sliderules. OK, this is something Heinlein did too. He had characters using log tables and sliderules for astrogation in Starman Jones. Granted, I don't know if anyone could have predicted mice or touch screens, etc. Still Heinlein came up with no-moving parts controls for the giant starship in "Universe" so he might have done something. But Turtledove should know better than to talk about iPods etc. Some of the repetition in other places could be used to imagine the technology of the future.
3) If the Cross-time corporation is so concerned about mention of the cross-time travel, then use some hypnotic suggestion or other techniques to help the characters not slip up. It won't catch everything, but give the characters some help. Like explaining that all passwords should not reference things knowable in the current time line, no matter how cute.
I think the slips that Liz makes are fairly natural, and actually are part of the growth of Liz's character. She learns the difference between ignorance and stupidity. I think all of that is pretty well done. Still, more training for Liz would be useful.
Dan is handled pretty well, I think. But if he really has any ambition or gumption, the things he has seen and learned should motivate him to want to improve things in his home area. If he were really wise, he would realize that working with the Cross-time folks, even in a limited way, would do more than railing against them. But that is a step well beyond where he is now. His reactions I think are pretty natural.
A cute little paragraph deals with the dissemination of scientific knowledge. I do, however, think that journals would get around faster than two years.
It is a good book and the series is getting better (Gladiator was very good.)
Kick it up a notch, Harry.