Nuclear energy is powerful, badly misunderstood and might prove useful in combating global warming, if people could just stop being pointlessly afraid of it.
The main lingering problem of nuclear energy is that it's associated with nuclear warfare and wastes and potentially deadly radiation. As a consequence, it suffers not only from weak public support but also outright opposition. Much of this is caused by an international and quite successful anti-nuclear movement, which was one of the major driving forces behind nuclear arms reduction treaties, but has nowadays degenerated into pseudoscience and fear-mongering.
See the FAQ on radioactivity and nuclear technology for answers to the most important questions on this subject.