The first chapter is called "2" because all the chapters have prime number names. That seems kind of gimmicky and inaccurate (it's not really the second chapter! argh!), but it's the content that truly determines whether this book is any good or not.
The opening paragraph is all right. I have heard that Haddon intended the narration to be dry and emotionless, and this is clear from the beginning. Christopher merely describes the scene of the dead dog lying on Mrs. Shears' lawn, giving no indication of how he feels, specifying for no reason that "It was 7 minutes after midnight". (That's the first sentence.) I assume he checks his watch a lot (he does; I read ahead). I also do that, though I'm not sure I'd be able to recall the information later in this fashion. Whatever. It's a book.
At the end of the paragraph, we get this:
I decided that the dog was probably killed with the fork because I could not see any other wounds in the dog and I do not think you would stick a garden fork into a dog after it had died for some other reason, like cancer, for example, or a road accident. But I could not be certain about this.
I don't know why he's overanalyzing the situation -- it seems pretty darned obvious what happened, but then I've known myself to follow similar thought patterns. Perhaps the more important question is why he thought it was worth writing down. I guess he wanted to cover all the bases so he didn't tell a "lie"... hey, look at me, I'm overanalyzing. Moving on.
The way these two sentences are structured is also very common in Twilight. We have an overly long sentence followed by a sentence fragment, which Dana describes on Reasoning with Vampires as "cauterizing" a sentence that should logically have included the fragment but would otherwise be so ridiculously long as to be arguably even worse. I don't like it. Autism does not cause bad grammar. There is no excuse.
I'm not sure how to feel about the emotionless thing. Maybe other ASD people do that, but I don't, and it's a stereotype. Our difficulty with cognitive empathy and self-expression makes us seem like we don't have feelings. There's no art to find the mind's construction in the face. On the other hand, at least we don't have a protagonist who keeps spouting things like "desolation hit me with crippling strength".
Anyway.
So Christopher goes through Mrs. Shears' gate and kneels beside the dog, and we find out that its muzzle is still warm, that its name is Wellington, and that it belongs to Mrs. Shears who is "our friend". I don't know who "our" refers to. Christopher's family, I suppose. Mrs. Shears lives "on the opposite side of the road, two houses to the left". Wellington is a black poodle, which explains the poodle-shaped hole on the cover that exposes part of a black page. "Not one of the small poodles that have hairstyles but a big poodle." Physical description is nice, but the "sentence" needs some work. It's a fragment, and there's something... off about it. I don't know exactly what should be done. More commas wouldn't do it any good, since there aren't any independent clauses in it anywhere.
Also, Wellington is called "it" even after being properly introduced, which I don't care for. His skin is "a very pale yellow, like chicken". I always thought chicken was more on the pink side, but maybe it's yellow sometimes. I don't generally interact with it.
The first chapter, or perhaps the second, takes up less than two pages. I guess the chapters in this book are going to be like the ones in Cat's Cradle. It ends thus: "I stroked Wellington and wondered who had killed him, and why." Finally the poor thing gets a gender. Unfortunately, he also gets an unnecessary comma.