Literature Flawed but fun
I'll start with the painful truth: David Weber is not, technically speaking, a good writer. His writing style is full of awkward constructs, purple prose and impossibly stilted conversations.
That said, I love the series, because while Weber's writing skill may be sub-par, his imagination is top-notch, and he managed to build a setting that combines relatively hard sci-fi with massive space battles.
This last bit needs a bit of explanation. Weber's sci-fi is 'hard' in that its rules are internally consistent and aside from a bunch of Necessary Weasel technologies, the laws of physics (and common sense) are generally obeyed. It still has FTL travel and gravity control, and it's much less hard on the biological side of things. But Weber's focus has always been on space, spaceships and the people commanding them, so that's where the reader's attention tends to be as well...and that's the part that hangs together extremely well.
A secondary (and growing, in the later novels) focus is on interstellar politics and the decision-making processes of governments and military forces, and this is one frequent source of criticism. Not only do these scenes run into problems with Weber's writing style (it's hard to imagine even people in the 4020s CE would talk like that outside of very formal occasions), they also frequently end up used as an opportunity to skewer one Strawman Political or another. Weber has strong political opinions on a number of subjects, and they can get somewhat grating at times if you happen to disagree with his views. And finally (probably the biggest sin in the eyes of disgruntled fans), they take away 'screentime' from the space battles. That said, they're not all bad and can be quite entertaining in their own way.
Weber has also collaborated with other authors (most notably Eric Flint), and those works are a mixed bag as well. Flint brings some fresh viewpoints (and some characters who seem to be in equal parts loved and hated by the fans) to the series but has his own problems with writing style and strawmanning, they're just different ones than Weber.
To summarize:
Don't go into this series expecting high literature, because you won't find it. You will, however, find some rather entertaining military sci-fi that manages to capture the reader's imagination despite all its flaws.
Literature "The Honor of the Queen:" A Disappointing Hero
This review is directed at the second book of the series, The Honor of the Queen. It was a disappointment. I enjoyed the first book, Basilisk Station — as another reviewer notes, it's not high literature, but it's fun. In Basilisk, Honor Harrington was a strong, proactive leader, always ready to spring into action with a clever plan. In this sequel, however, she is a thoroughly unconvincing hero who makes silly, costly mistakes and then spends ages moping about them while the audience is heavy-handedly invited to sympathise with her. Of course Harrington triumphs in the end, but it feels less like her winning, and more like her enemies losing — the villains of the book are carrying a planet-sized Idiot Ball.
Some of the villains are well-written and sympathetic — the Havenite officers, who carry the other villains, the backward (and truly evil) Masadans like the mother of all Loads. But the Havenites are a bit too sympathetic — by the end of the book the impression is that they are actually smarter and better than Harrington, and that they deserved to win. They are simply too weighed down by allies who practically hand the victory to Harrington — again and again.
In Basilisk, Harrington triumphed against the odds because she was smart and tough and competent. In this book, her Havenite enemies are the smart and competent ones, and Harrington triumphs only because the odds are stacked in her favour.
The other conflict in the book is between Harrington and her own allies, the extremely sexist Grayson culture. This could have been a very interesting aspect of the plot — but the author really wants us to like the Graysons. Thus, much of the friction happens behind the scenes, with the reader hearing about it second-hand. All the Grayson characters we actually get to know in any detail happen, of course, to be very open-minded, practically eager to realise their error of their ways and accept women as equals. All the really sexist Graysons are flat background characters we barely see. What could have been a very interesting conflict ends up being unconvincing.
In short, this book has unconvincing characters, an unconvincing plot, and a hero you don't want to root for. It made me unsure whether I want to continue with the series.