These all are valid points. From the technological point of view nuclear technology is pretty safe and the margin of error is rather low. There are many redundant fail-save measurements to retain a save operation. But if something will happen, it will be devestating. Most famous incident is Chernobyl. Also, nuclear waste management is a huge issue. Not many (if any) locations for waste storage have the capability for eternal storage. The Asse II mine for instance is a former salt mine which has been re-purposed as a deep geological repository. It was supposed to last alt least several thousand years. After only 30 years of usage it has been detected that water seeps into the vault which leads to corrosion of the barrels filled with nuclear waste which ~~will result~~ already resulted in a release of radioactive elements. This is how the barrels were handled and stored. I am no expert but thirty years into almost eternity is a pretty bad figure.

And there is another thing - and in my opinion this is a really serious one: Nucular power plants are operated by corporations within the private sector. This means that such a power plant is conducted with an economical focus (= profit). The incentive to make profit will result in skipping maintenance, bribing inspectors and downplaying any technical difficulties. Even when assumed that all the other issues (waste management etc.) are solved, every technical malfunction that resulted in the leakage of radioactive material woult be not be made public voluntarily. There were many incidents that have been made public, because the law required them to do so.. The hidden number of incidents that were not required to be made public is probably much higher.