It has been said so often that it probably qualifies as an urban legend: when Secret Service agents learn how to detect counterfeit banknotes, they don't spend months studying lots and lots of counterfeits to learn what counterfeits look like. They spend months studying real money, learning all the nuances that make real money look real. That way, if a counterfeit comes along that lacks those subtle characteristics, they instinctively know there's something wrong with it, even though they may not be able to point the finger at exactly what is wrong with it without careful analysis.
It is, perhaps, an oversimplification - you do need some experience with known categories of counterfeits to help ID them faster. But "experience" is what it all boils down to, experience in handling lots of genuine coins or notes as well as basic knowledge of counterfeiting techniques.