Simon says economists should study the history of economic thought. I'm with him: my masters' dissertation was on Malthus's theory of unemployment. But this poses the question: why bother with the wrong ideas of dead men?
One answer is that they weren't always wrong. Marx was right about quite a lot. Mill can be read profitably by anyone worrying about the consequences of a low-growth economy; Ricardo anticipated today's debates about automation; and you can read the rise in commodity prices and fall in equity valuations of the last 10 years as being consistent with his theory of rent and profits.
And sometimes, the difference between the classics and modern economists is not that the latter are right and the former wrong, but rather that they address different questions. Ricardo didn't much care about year-to-year fluctuations in GDP but did worry a lot about the determinants of the distribution of income. Many economists today have the opposite priorities. This, though, means their abilities to address Ricardian and Marxian issues have ossified. If you read Greg Mankiw's defence (pdf) of the 1%, you'll not get the impression that today's economists have a much better understanding of the distribution of income than Ricardo or Marx did.
In fact, in one sense economists are only now rediscovering what the classics knew. All of them, from Smith with his invisible hand through to Marx, were concerned with the question of how some kind of order emerged from what looked like a chaotic process of millions of people exchanging millions of goods. To Smith, this order was benign, to Marx less so. But both agreed on rthe importance of the question: how does order emerge from millions of individual decisions? Neither thought that a "Robinson Crusoe economy" made sense. It is only quite recently, with the growth of interest in markets as emergent evolutionary (pdf) ecosystems (pdf) that this issue has returned to the forefront of economics.
This raises the question: in what ways has economics progressed? One answer is that we've gathered more hard data than the classics had; Smith, for example, relied almost solely on anecdote. Another, obvious, answer is that we have vastly more mathematical formalism than they did. But what is the value of such formalism. Could it be that there are some questions which can't be answered solely by reliance on mathematical technique? Studying the classics reminds us that there are potentially more tools in the economists' shed than maths alone.
What's more, even when the classics are wrong, knowing why can sharpen our understanding. For example, everyone from Malthus to Marx expected the economy to converge to a state of zero growth. This view has been wrong (so far!) because technical progress has won the race against diminishing returns. But this should force us to ask about the determinants of such technical progress; why is this more powerful than the classics thought? It is only quite recently - with the emergence of endogenous growth theories - that economists have progressed from Malthus; the old neoclassical growth models merely assumed technical progress which is no explanation at all of the classics' failure.
And herein lines another reason why the classics matter. They were the smartest people of their day. If they were wrong or confused, isn't it also likely that the best minds our our day might also be mistaken and inadequate? The idea that we are clever and our forebears stupid is surely just arrogant gibberish. The mere passage of time does not ensure that progress happens. If this were the case, we'd have to believe Rihanna is a better singer than Bessie Smith was. And nobody believes that.