The Bureau of Labor Statistics does precision guesswork. They'll be happy to tell you the unemployment rate down to a tenth of a percentage point. And they probably get close, or at least as close as humans know how to make those things.
I hope no one believes that they actually run around and count noses every month. It's a sampling thing. They take surveys of employers, and they munge the data with some statistical algorithms to (hopefully, but never exactly) correct for sampling bias and other errors. Then they adjust for seasonal factors, like H&R Block's huge rise in employment in March and April, followed by a huge layoff on April 16th; and of course the Christmas Winter Festival stuff.
In recent years, people operating as independent contractors instead of employees have become a big deal. The BLS has no clue how much of that there is. I probably look to them like one of those guys who quit his job and then gave up trying to find a new one, so they longer count me among the "employed." Meanwhile, I'm making money, growing my business, and having more fun than I have had in a long time.
The point of all this is that they have to guess about a lot of things. And depending on which guesses they include or do not include, the unemployment rate could be up or down by a point-and-a-half. It's not that they are "wrong," it's just that no human knows what the right number is,. The BLS is as good a group of guessers as anybody else has.
I don't think it is true, as you suggest in #39, that using your friends and acquaintances as your sample has more "real world validity" than what the BLS does. They use a sample too, and theirs is a lot bigger than yours, and is expressly designed to capture regional variations, seasonal effects, specific-industry effects (9/11 happens, people stop travelling, airlines go into the tank, it all pops out 2 years later as layoffs concentrated in cities with big aircraft manufacturing plants.) No humans are perfect, but those guys do know what they are doing.
What really matters from a "what do we do now?" standpoint is not whether unemployment is 5.9 or 5.7 per cent, but whether it's going up or down. So long as the BLS picks a methodology and sticks with it, such that whatever errors they have are in the same ballpark from month to month, we can use their percent change data with reasonable assurance that it's "close enough for government work."