On his blog today, Tyler Cowen responds to the question, "What is the biggest flaw in the labor theory of value?" Tyler does list some sophisticated flaws that have to do with capital and other inputs, but here's my candidate:
According to the labor theory of value, the value of something is determined by the amount of labor used to produce it. So consider the following case. One man goes out panning for gold and at the end of a 10-hour day has enough grains of gold to make an ounce. Another man goes walking along and in 1 minute, trips over a stone. He picks it up and it's a gold nugget. Labor input? Ten hours vs. one minute. Value: the same.
Maybe that's what Tyler meant when he said "inputs are heterogeneous." But the point is that he left out randomness.