In hindsight, this book has two big things working against it, which I'll assume accounts for the many vehemently negative reviews.
The first is the nostalgia for the orignal, "Rosemary's Baby", which as a film and as a book, was an unexpected little gem of a horror story. It was very unconventional in that the bulk of the book was just the mundane comings and goings of a young couple living in New York City. The genius of it was that amidst all rather run-of-the-mill banality, there were hints of sinister goings-on, which pay off with an absurd and shocking twist ending. The Roman Polanski film captured the tone of the book almost perfectly, and thus, for forty years we've had this perfect little horror oddity that has become almost iconic over the decades. That the author would want to come along after so many years and write a sequel is a dicey proposition. How do you follow up the lighting-in-a-bottle that was the original?
Well, Ira Levin takes a rather novel approach, which, in my opinion, is a reservedly successful one. Instead of taking the same tact as "Rosemary's Baby", and writing the story of a mundane protagonist with hints of something more creepy, he takes Rosemary and places her in a far more outlandish setting: she wakes up at the beginning of the novel from a coma she's been in for thirty years, to find that her half-demon son, Andy, has become the figure-head of a global peace movement. She and her son are world-wide celebrities.
I'm sure that fans of the original novel were shocked, and understandibly upset by this drastic change in backdrop. I almost said change in tone, but the tone is almost exactly the same. Though she's a global celebrity, most of the book still deals with the rather boring details of things like Rosemary getting her hair done, going on a date with one of Andy's entourage, jogging in the park, and whatnot. Similarly, there is a sense of hidden mystery like the first book, this time bolstered by the fact that you know Andy is the son of Satan, and quite possibly, the Anti-Christ. Ultimately, it is only the setting that is different from the original.
Probably to my benefit, I did not go into reading "Son of Rosemary" as a longtime fan of the original. I read it immediately after reaing "Rosemary's Baby" for the first time, so it almost didn't feel like reading a sequel at all, just additional chapters of the first. And read like this, I think the second book holds up rather well. As I said, the tone is very similar from one book to the next, and read back-to-back, it is a very smooth transition from the world of the first to the very different world of the second.
Which isn't to say that it is a perfect read, and this is the second main reason why I think this gets so many bad reviews. The writing seems very rushed. Whereas "Rosemary's Baby" fleshes out all of the major players (Rosemary, Guy, Minnie, Roman) and lets the many other Bramford residents float around rather underdeveloped in the background, "Son of Rosemary" really only gives any decent time to Rosemary and Andy, while many other characters, who would seem to have important roles in the plot are given rather short-shrift. Because of this, seemingly important moments in the story (a murder, a pretty significant plot twist) don't quite carry their intended weight. Also, there are an aweful lot of characters floating around that don't seem to do anything besides clutter up the background.
Along a similar vein, the underlying mystery of the novel is an interesting one, but pretty obvious and is never really fleshed out. Its almost as though Levin had this great idea for a sequel, but then decided he's rather do something else than write it all down. So what we got was a brief sketch of a broader picture.
[SPOILER] And concerning the big ending (the one after the 'shocking' plot twist), I have to disagree with everyone claiming Levin took the punk's way out and just made the whole thing a dream. I thought it was pretty clear that Rosemary getting to go back and relive her life with Guy was her payment from Satan for not fighting him on the whole end-of-the-world plan he was carrying out. She at first refuses to abandon Andy, but her son tells her to go, and to trust him, and moments later, she's back in 1966 with her long-lost husband. I don't think that was a cop-out at all. I actually kind of like the idea of Rosemary letting the world end while she gets to go back and have her life over agian.[END SPOILER]
So in the end, no, "Son of Rosemary" is not as good as the original, mostly because the original was such a unique gem of a book. But it also seems more hastily written with many interesting ideas only briefly addressed which doesn't exactly ruin the book, but leaves one with a feeling of missed opportunity.