Would a scatter shot or buck shot perform better?
One would assume that's what's loaded in any shotgun. It pretty much guarantees a hit at close range, but you're still only going to hit one zombie. At the range Jamie was shooting I don't think buckshot would disperse more than a couple of inches.
Well it's not enough to hit a zombie, you need to destroy the brain, so I think in anything other than point blank range, birdshot is going to be useless. Even buckshot may be of limited use as accuracy drops off rather sharply at the 10-15m mark IIRC.
Of course the whole point of a shotgun is that it's not meant to be accurate, so it's far from the optimal weapon for this kind of job. It's been a while since I've read WWZ, but if memory serves the author reasons that the best ranged weapon for this kind of thing is a small calibre semi-auto rifle. Even then, when faced with a large horde the idea is to form a firing line or square.
When faced with horde alone the best thing to do is not use a gun a all if at all possible. Mostly, stay quiet, stay hidden and the weapon of first recourse is always a blade....I really need to read that book again sometime. All this talk of killing zombies is making me all nostalgic!