How Few Remain was a very good stand-alone, and the hint that there would be a German-US alliance in the future made me look forward to more books set in the 1900's even before I realized HT had this series in the works.
Then the disappointments began.
My biggest disappointment with the whole series was a sense of missed opportunities. Turtledove began with a well-reasoned, plausible, and interesting background of global alliances with the USA and CSA logically on different sides. His extrapolotations of culture and society in 1914 USA and CSA was also well imagined, and the impression given that North America and the world in general was less prosperous and more autocratic than OTL rang true. I also rather liked the fact that neither the USA nor the CSA was presented positively, and that there was not a clear or positive end to the series. I saw the books as both a critique (as Thande mentioned) of American exceptionalism but also an implication that, without a unified and democratic USA, the 20th century would have been even worse overall.
Such an interesting 20th century deserved to be presented (at least occasionally) from a global perspective - both with knowledgable PoV characters and narrative devices such as newspaper articles, chapter prefaces, and the like. Instead, he populated the series with an almost infinite number of "plain folks" PoV charcters, many who were redundant, and most of whom could barely see beyond their own noses. Some of the characters, especially those that explored race relations and the culture of the increasingly genocidal CSA, were very interesting, but I could have done with a lot fewer frontline grunts, housewives, and the like saying the same things all the time.
What could have improved the series in my mind:
1. Put the whole 50-year span into at most 4 books, one each focusing on a key period in this history, rather than draw it out as a nearly year-by-account.
2. With a few exceptions (Scipio, Featherstone, and some of the "real" people,for example) don't keep the same PoV characters in each volume. Also, make more use of high-level characters (chancellors, ambassadors, presidents, foreign ministers, etc) to tell the broad historical narrative.
3. Although I understand that the purpose of the series was to explore an alternate North American, not world, history, I'd have liked to see more from the European side of things...but please not from PoV characters in the trenches!
4. While I think the historical parallelism in the series (the almost one-for-one duplication of OTL WW1 and WW2 events in North America down to the holocaust) was a legitimate literary device to emphasize Turtledove's views about American exceptionalism and not intended as an effort to present a plausible alternate history (something with which I have no objection), it was overdone to the point that it almost became comical. Surely he could have created campaigns and battles that in concept were unique to this TL (naval battles on the Great lakes with mini-dreadoughts for example, or combatants employing different technologies that were explored or considered in OTL (zeppelin aircraft carriers, cruiser submarines, hybrid cruiser/carriers, etc).
