So the premise of this book (as the narrator keeps helpfully reminding us) is that this group of three children will continue to have difficult problems to overcome, and every time they succeed in dealing with one problem, another will crop up. In the writing business, this is what's known as 'a plot'.
But then he takes it one step further: in addition to all the difficulties along the way, he assures us that the characters will never break this pattern, and there will be no 'happy ending'. I think this is a good idea, especially in a children's book, because we, as a culture, don't have enough role models for failure.
We have lots of role models for how to behave when we win, but this isn't really very useful--it's not when we win that we most need guidance and aid. We need more examples of how to maintain, how to persevere, in the face of failure.
At this point, our only role models for what to do when we fail are villains, who tend to get angry, yell, whine, take it out on subordinates, and then develop vengeful plans to make everyone feel as bad as they do. The unfortunate result is that people often begin to act like villains when things don't go well, an effect which can be observed most easily by holding a job where you have a boss.
So I'm all for 'no easy wrap ups' at the end of the story, but unfortunately, Snicket is unable to develop a conclusion without this easy route. It takes a very skilled writer to eschew convention and still write something interesting, and his reasons for avoiding standard practices should not be merely to differentiate himself, but to achieve some alternative goal for his story.
There are authors who have achieved this, even in children's fiction--Lewis Carroll and Roald Dahl being the preeminent examples. When Snicket laid out the premise of his books, I began to look for something along the lines of those two authors, who, despite creating stories of children suffering constantly and unfairly, managed to write entertaining, enjoyable stories.
But then those stories were wild and vivid, even when they were dark. Dahl's ability to create grotesque, powerful characters made for dynamic, engrossing stories, while Carroll's quick, fertile mind kept us always guessing, and often laughing, despite Alice's constant frustrations.
Though Snicket is trying for a witty style, he rarely gets there. After the second chapter, all his jokes have already been established, the rest are only minor variations on the same themes. There are no surprising insights to back up his humor, nothing unexpected, just a continuance of the same tone: dry, but not acerbic.
The characters, likewise, show little variance. The vocabulary and speech patterns are all very similar, whether adults, children, villains, or heroes. We are often told of differences in character by the narrator, but these never actually make it into the characters' mouths.
Since the characters are fairly cliche and undifferentiated, Snicket cannot hang the plot on them, like Dahl would. They cannot provide the vibrant impetus for the plot, so Snicket's plot instead becomes a series of convenient (or conveniently inconvenient) events.
The writing itself is not bad, it's mostly just a case of Snicket not being clever or dark enough to buoy his premise. In the end, not much stands out, not the characters, nor the humor.
I applaud his attempt to address difficult and painful issues in his books, and without resorting to basic melodrama, but tragedy is measured by the subject's capacity for pain, so characters must be vivid and deep in order for events to feel truly unfortunate; otherwise, it just becomes the same array of problems common to every plot.