One thing to remember: the unemployment figures are the result of polling. The Bureau of Labor Statistics doesn't count every single job in America; they call 60,000 households and extrapolate. So the result, like any poll, has a margin of error -- in the BLS' monthly report, it says that a move of 400,000 is required to be "statistically significant," which gives you some sense of the margin of error they are assuming.
Anyway, it may be worth noting that the government isn't the only outfit that polls employment. So does Gallup. Their result for September 2012?