There is good reason to pay more attention to scientific experts than to amateurs, so long as science is based on experiments. Only trained experts can do experiments with the care and precision that experiments demand.
This appears to me to be, at best, a non sequitur. The problem with cranks is not that they are careless in design or execution of experiments. Carter's problem is that he doesn't have a theory.
Does anyone have any idea what Dyson meant?
Presumably the stuff scientists learn by apprenticeship, per Teaching The Unteachable (EY noting that 155 out of 503 Nobel laureates were the students of Nobel laureates).
Freeman Dyson writes in the New York Review of Books about people who took up the crackpot offer. Not just complete cranks, but eminent scientists such as Eddington who got into crankery in their later years.
New thing I learnt: Dyson was not only a good friend of Immanuel Velikovsky, but considers him a greatly underappreciated poet.