Two things: first, it has to be refueled. Uranium doesn't last forever. It does last a long time though. Second, neutrons are released during the fission. These neutrons interact with nearby material and cause small cracks. This makes the material brittle (neutron embrittlement.) Embrittlement may result in component failure.
Lead shielding would probably be counterproductive in a rocket. Well, if they can design so the structure holds together long enough they might get some use out of this.
The ion or plasma propulsion idea is much better as far as ISP if you don't need a lot of thrust in a short period of time. The thing is that once in earth orbit you wouldn't necessarily need high thrust to go somewhere, just steady thrust for an extended period. If they want to use a nuke for power in an ion motor, they could, but solar cells also work.