For a quick sample, here's what Mankiw had do say on what economists don’t understand about politicians, and vice versa:
I don’t think economists fully understand the set of constraints that politicians operate under, probably because we have tenure, so we can say whatever we want. The politicians don’t. They constantly have to get approval by the voters, and the voters have different views of economic issues than economists do. So the politicians are sort of stuck between the voters they have to appeal to and the economists who are giving them advice. I think understanding the difficult constraints that politicians operate under would be useful.
In terms of what politicians don’t understand about economists, I think they often turn to (economists) for the wrong set of questions. My mentor, [Princeton University economist] Alan Blinder, coined what he calls Murphy’s Law of economic policy, which says that economists have the most influence where they know the least, and they have the least influence where they know the most.
Politicians are constantly asking us, ‘What’s going to happen next year?’ But we are really bad at forecasting. I understand why people need forecasting, as part of the policy process, but we’re really bad at it, and we’re probably not going to be good any time soon. On the other the hand, there are certain problems where we kind of understand the answer. We understand that rent control is not a particularly good way to run a housing market. We understand that if you want to deal with climate change, you probably want to put a price on carbon. If you have a city that suffers from congestion, we can solve that with congestion pricing.