Probably just got a lemon. Exchange it.

I'm not sure what kind adjustments Sheldon recommended, but the only real adjustments these things usually need is more grease. Not a terribly hard job, but a little more complicated than, say a front hub. I'd venture to guess you're not all that familiar with bike mechanics. Best bet is exchange.

Coaster brakes are actually extremely reliable, commonly providing years of service with little or no maintenance. They are extremely mature technology, hugely mass produced, and thus, very inexpensive. Around here, they seem to be the preferred setup for the commuting hoi polloi, for reasons of simplicity and reliability. I would not say they are underdesigned. More accurately, they are adequately designed, and no more. There is effectively no such thing as a "quality coaster brake hub". 99% of all currently manufactured coaster brake hubs in the US are pretty much identical regardless of name. There is one brand manufactured in Europe occasionally found in the US that is different, appearing to be more nicely manufactured. However, in use, it offers no actual advantages, other than looking nicer.