The book the selfish gene has the effect on people who accept it, to serve themselves in stead of others.
You have evidence of this? Did it have this effect on you? To the contrary, the book demonstrates that behavior that is better for the group but negative - even fatal - for the individual can be selected for, genetically.
Intentions are much besides the point, although as I've shown Dawkins apparent and stated intentions with the book are not those of a regular scientist just wanting to provide accurate knowledge.
I don't think Dawkins' intention was anything but to sell books. To do that he needs an engaging read, aimed at the comprehension of people who tend to buy the most books - laypersons. Dawkins isn't trying to do science here, but rather to explain science in an engaging way.
The book says that all organisms are basically selfish, and there are some *exceptions* of altruistic traits.
The book in fact says that
genes are selfish, not organisms (hence the title "The Selfish Gene", not "The Selfish Organism".) Altruistic behavior can be considered "self-serving" from the perspective of genes. What about this aren't you getting?
Honestly I haven't even read the book (I've heard the explanations though) and I know this. Your arguments are pretty weak unless you can quote direct passages that support your claims.