How accurate is DNA testing really?

Just shooting from the hip on this one, folks. No real research done by myself here. Just read this article from the L.A. Times and it made me wonder.

You know, when they say such-and-such a match has a statistical probability of 1 in a 113 billion, what does that really mean?

It doesn’t mean impossible. Just improbable. And if the improbability calculation is built on faulty premise, then the number means nothing at all.

Should DNA testing be pulled down from its lofty pedestal in courts of law? Right now, it seems kinda incontrovertible:
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“We have DNA evidence that puts you at the scene, Mr. Mandu.”

“No, but wait, I wasn’t there. And it’s just a statistical probability you’re using.”

“Yah, try that line of reasoning on the jury. Buwahahaha!”
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Increasing the number of required locus points seems to help make the statistical probability more palatable. But does that really solve the problem, or just tackle one of the symptoms?

There’s no perfect crime-busting tool. No silver bullet that only kills the criminal. Can coincidence only ever be limited, not eliminated?