How do economists measure the success, or shortcomings, of the economy?

They have an aggregate demand line which means also the expenditure line of the economy. Based on the definition, it is consumption + private investment + government purchase + net exports. So if this line cuts the 45 line, it would be an equilibrium, means success. If it does not cut, it would mean a shortcoming. But it might not be the real success because the real GDP might not equal the potential one.

Alas, nothing is perfect. And GDP is no exception. As much as economists like to use GDP as a measure of output, or even as a measure of a country's well being, GDP has some limitations when trying to answer those questions. GDP leaves out some production in an economy, such as the squash your mom might grow in the backyard, or other non-marketed goods. Even though GDP is frequently used to capture the wellbeing of a society, it was never intended to do that, and as a result it leaves out important aspects of well-being like pollution or even happiness.