The author describes the novel as having a sort of external third-person viewpoint ...
I found an interview with Neil Gaiman in which he says that Shadow isn't like most point-of-view characters: we don't get inside his head much, but rather experience events together with him.
I actually wrote the entire first chapter in the first person. That was my first try at Shadow. It really felt odd. It didn't feel right. So I put it aside for a while to figure out what was wrong with it. I then realized that this is a character that we really need to see from the outside. Yes, we're going to be with Shadow throughout the books. I also began to suspect that at the end of the book we were going to have to follow some other characters around, I wasn't sure how reliable a narrator he would be. For the body of the book, we do see everything Shadow does, not exactly through his eyes but standing next to him, so to speak. He was a very weird character to write.
From this perspective, perhaps it makes more sense that Shadow seems underdeveloped. We're not seeing that much of his personality and soul because he is by nature a private person, not opening up easily to others, and - even though he's the protagonist - we're not really properly inside his head.
... and describes Shadow as a 'mirror', reflecting others rather than projecting himself.
In the same interview, Gaiman says:
One of the strangest things I found when writing Shadow is that he has no personality unless he's with somebody. At which point he will adopt a personality, or occasionally mirror them. His speech patterns are ever so slightly flexible. People would get very confused. Someone who's in the middle of the book said about Shadow, "But he's just this big, dumb guy." "No, he's not," I say. "He was with big, dumb guys at the time, so he was talking like a big, dumb guy." There are some lovely little weird moments. I love the moment when he pretends to be Andy Haddock, head of A-1 Security Services, for a couple of paragraphs and he has some wonderful little conversations with various people.
It's also worth noting, though, that Gaiman sees Shadow as one of those characters who's really taken on a life of his own. He describes in the afterword to the "author's preferred edition" of American Gods (I don't have the book to hand right now, but will add quotes later) how Shadow was difficult to write; he seemed such a fully-formed character that he could only be written in 'his' way and would reject others. This should probably be borne in mind when considering the reliability of the author's word about his character: even Gaiman himself says that Shadow is his own separate entity rather than just a facet of the author's mind.
But of course, the apparently featureless Shadow ends up being the centre-point of events.
Perhaps, by taking Shadow at face value as a featureless, characterless "blank slate", you're making the same mistake that Odin and Loki did when they underestimated him. He's not just the dumb lackey that Mr Wednesday used him as; he has his own kind of power, and his own intelligence, which enabled him to see the real purpose of the war where all the other gods had failed.
Perhaps this is exactly the point. We don't see his inner thought processes, or much depth to his character, but he ends up having strength and insight which everyone else lacks. Doesn't this give us the impression of a man who keeps himself to himself but who nevertheless has intelligence, emotions, and personality, just not that he chooses to outwardly display? And isn't that exactly the type of man Shadow is supposed to be? Surely it's a good portrayal, then. It's much harder to convey the sense of a character being a 'closed book' if you also show the readers all their thoughts and feelings.
As this reviewer puts it:
Shadow has many roles. Gaiman has created a character who, by all appearances, seems to be an average, somewhat uninteresting guy. As we read the novel, Shadow's character become more and more complex and we realize how he is the pivot on which the story turns. [...]
Part of Gaiman's brilliance in creating Shadow's character is that Shadow's character seems to be flat and boring. [...] But Shadow goes through great trials and is the pivot point of this novel. Everyone in the novel is centered around Shadow in some way. As we get to know Shadow we realize how complex he is. Sometimes it seems that the book is really about Shadow and his personal transformation, and the war between the Gods is just a backdrop for Shadow's story.
