There should be exactly ONE problem with nuclear power, and it's the long-term question about spent fuel rods (radioactive 'stuff'). Personally, I think if we had a few groups that solely built and ran nuclear power stations and we had scheduled, unmanned launches of the waste materials into space, nuclear would power the world.
Any and every bad nuclear 'event' is due to gross human error. That fact that its gross makes it avoidable. Also, is it wise to build on a fault line by an ocean? Probably not. But there are so many safeguards to avoid any type of serious meltdown that it's nearly impossible for it to happen.
There are many other challenges with nuclear.
1. It's no longer cost-effective. Ohio is about to pass a bill to subsidize its nuclear plants (and coal plants, which makes no sense whatsoever). This is true of many existing plants and even moreso for new plants (again, the Georgia plant debacle being a prime example while all other new nuclear projects have already been canceled).
2. It's inflexible (ie. on or off). I used to think this was for technological reasons, but it's actually also due to economic reasons. Nuclear generation is only cost-effective when generating at its capacity whereas other sources of generation can operate more flexibly. With the rise of wind and solar generation (which can only be controlled through curtailment and combining it with energy storage), flexibility is increasingly important, since electricity supply & demand must be balanced at all times.
3. They take a long time to build. Even putting aside the other issues, nuclear plants take longer to build than any other type of generation. Furthermore, they also take a long time to decommission, too. Of course, few people want to live near them, too.
4. There is a shortage of nuclear engineers, and most of them are older. There aren't many people studying to become nuclear engineers, because people realize that there isn't a long-term future in it compared to other technologies.
