The only thing is that they take up a hell of a lot more space and are a lot more unsightly than "dirty" power plants. Nuclear power is great, the only quandary is what do we do with the spent fuel rods since they're radioactive for about another 10,000 years.
Nuclear meltdowns like what happened at Chernobyl and Fukushima wouldn't happen in the US. The only nuclear accident we've had was Three Mile Island which is nothing compared to the above two. Also terrorists attacking nuclear power plants wouldn't happen either because the walls of pretty much every reactor in the US are like 30 feet thick of reinforced concrete, they can withstand direct hits of a 747 or a missile (my dad worked on the one here in NJ), if an ICBM with a nuclear payload is targeting a nuclear plant, we're already fucked.