WASHINGTON—The unemployment rate drops. Productivity grows. The trade deficit shrinks. Sounds great, right? Not so fast.

Borrowing radio broadcaster Paul Harvey’s signature saying: let’s hear the rest of the story.

Some seemingly good economic numbers can be something of a mirage masking weaknesses in the national economy.

Let’s take the unemployment rate, which dipped to 5 percent in April, from 5.1 percent in March. A closer look reveals that the decline in unemployment is not as good as it looks at first blush. The drop came as the number of people holdin...