What's Wrong with Plutonium?

Because it emits alpha particles, plutonium is most dangerous when inhaled. When plutonium particles are inhaled, they lodge in the lung tissue. The alpha particles can kill lung cells, which causes scarring of the lungs, leading to further lung disease and cancer.

Is it safe to touch plutonium?

People can handle amounts on the order of a few kilograms of weapons-grade plutonium (I personally have done so) without receiving a dangerous dose. You don't just hold bare Pu in your bare hands though, the Pu is cladded with some other metal (like zirconium), and you generally wear gloves when handling it.

Why don't we use plutonium?

While of a different order of magnitude to the fission occurring within a nuclear reactor, Pu-240 has a relatively high rate of spontaneous fission with consequent neutron emissions. This makes reactor-grade plutonium entirely unsuitable for use in a bomb (see section on Plutonium and weapons below).