The scientists and engineers who design and run nuclear power plants are highly trained and skilled. So surely we should take their word for it that nuclear power is safe and economical? This is a very understandable point of view, so here are some reasons why we should very definitely NOT leave it to the 'experts':
Starting with the obvious, anyone who undertakes the lengthy training to become a nuclear engineer and works in the sector is unlikely to oppose nuclear power because it means throwing away their skill set and career. Also familiarity with a technology makes you trust it more - most people who drive frequently but fly seldom, feel less nervous in their car than they do in an aeroplane (though in fact the plane is statistically safer).
Secondly since when were engineers cautious and restrained? Engineers are usually male: most boys like things that are big, fast and go bang, and many of us continue this into adulthood - why else the large numbers of ridiculously over-powered motorbikes and sports cars on the road. Engineers can often recount hair-raising, irresponsible 'experiments' that we carried out in childhood. The natural engineering mentality is "If we can do something - we want to do it". Some readers may find it hard to believe that whatever they had done as children, highly educated adults might want to do crazy things ... so let's take a look at some examples in the nuclear egineering field:
For about 5 years from 1958 the United States worked on project to design spaceships powered by dropping atomic bombs out from the (very thick) bottom of the spaceship . Each bomb would explode a short distance underneath the ship, blasting it higher. Between 500 and 1000 bombs could be required for single flight. The idea would permit bigger and faster spaceships and promised 'cheap interplanetary travel'. If atomic bombs ('A-Bombs' or fission bombs like the one that destroyed Hiroshima) were not powerful enough, more powerful nuclear fusion bombs (H-Bombs) could be used!
Now this idea may be perfectly feasible and there is part of me that would love to see such a rocket work (though preferably from a very long way away!) ... but as sensible adults should we contemplate for even a minute having spaceships raining nuclear bombs behind them flying through our skies? What if one went of course or crashed? What about the radioactive fallout - the fallout from the two bombs dropped on Japan killed tens of thousands.
Desperate to find a peacetime uses for their terrifying technology, nuclear scientists in both the United States and the Soviet Union proposed using nuclear bombs for excavating canals and harbours by simply blasting the earth out of the way. In the U.S. a project called 'Plowshare'  was set up for this purpose. It considered proposals for creating a new sea-level canal in Panama using over 300 atomic bombs; another plan was to blast out a harbour in Alaska with five nuclear H-Bombs. Altogether 54 schemes were considered, including using nuclear bombs for mining or creating underground storage chambers. While none of these were carried out, over $700 million was spent and several nuclear bombs were detonated in Nevada to test the ideas.
From the 1940's to the early 1960's the U.S. Air Force and the Atomic Energy Commission spent more than $7 billion trying to develop a nuclear-powered bombers that could stay in the air for weeks. The bomber was to use a high-temperature 'fireball' reactor fueled by molten uranium salts. Tests were made with a B-36 bomber converted to carry a live three-megawatt air-cooled reactor. Heavy lead and rubber shielding protected the crew from the reactor behind them but to avoid extra weight the other sides of the reactor were left to emit radiation unshielded!.
The New Scientist reported in 2003 that US Air Force is once again examining the feasibility of a nuclear-powered aircraft, but this time unmanned. "The USAF hopes that such a vehicle will be able to "loiter" in the air for months without refuelling, striking at will when a target comes into its sights. But the idea is bound to raise serious concerns about the wisdom of flying radioactive material in a combat aircraft. If shot down, for instance, would an anti-aircraft gunner in effect be detonating a dirty bomb?"
The Ford Motor Company developed a nuclear-powered concept car in 1958. It was to be powered by a small nuclear reactor in the rear of the vehicle. However Ford very sensibly never built any working models of the "Ford Nucleon".
Radioactive waste from nuclear power stations needs to be isolated for thousands of years. Engineers have managed to find 'uses' for small amounts of this waste, but once again it is often hard to see how the supposed benefits outweigh the risks.
The radiation from waste kills lifeforms so it can be used to sterilize things. An industry has built up, eager to irradiate the food we eat in order to kill bacteria or insects, or delay ripening of fruit. Many however believe that irradiation damages food and could cover up poor hygiene practices because any degree of contamination could be compensated by irradiation.
The heat given off by waste has been used to power the lights on some of the buoys used to guide shipping: where better to put dangerous radioactive waste than in some buoy out in the ocean, secured only by a rusty chain and where any stray ship can crash into it ... and all to save the cost of someone occasionally having to change a normal battery. Happily nowadays solar panels are the usually the first choice where you need to power something in a remote location. Ironically buoys have now been developed that are wave power devices and generate substantial amounts of electricity themselves.
So our conclusion must be that there are plenty of engineers and scientists who are perfectly willing to work on projects verging on lunacy for as long as the politicians pay them (with our money) to do so. Some of these projects were stopped so we don't yet have rockets raining atomic bombs behind them as they soar into space. But we do have hundreds of reactors dotted around the world which generate material for dirty bombs and atomic weapons, which produce waste that we don't know what to do with and is dangerous for pretty much eternity, and which could render much of the globe uninhabitable if they are destroyed by accident or war. Sanity has not broken out yet.
Finally we should note that some of the engineers and scientists who have worked on nuclear technologies have come to have grave concerns about the dangers. One such was Dr. John Gofman, the pre-eminent Manhattan Project nuclear scientist and medical physician who said "Licensing a nuclear power plant is in my view, licensing random premeditated murder."
 Nuclear bomb spaceships. See Project Orion in wikipedia.
 Nuclear excavation and project Plowshare. See: Phys Org - Geography professor writes first in-depth account of scheme to engineer with atom bombs; wikipedia - Operation Plowshare.
 Atomic Planes now. See: The New Scientist - Nuclear Powered Drone Aircraft on Drawing Board.
 Irradiated food. See The Food Commission - Irradiated Food.