Is this possible? (nuclear propulsion)

Yup. Back in the 80’s Discover magazine printed an article about an experiment ran on one of the shuttle’s missions. A minature smelter was built which would melt and cast metal on the shuttle. One of the interesting things they discovered was that the resulting casting was stronger than one made on Earth. It’d be a little more complicated to build a lunar smelter than an earthly one, but potentially, the materials yielded could be better than those from the Earth.

I doubt you would find materials suitable for fission on the moon, but materials suitable for fusion are in (relative) abundance, if someone comes up with a fusion based system of propulsion.

Hmm, so assuming we could overcome all the radiation and such and get this beast airborne (spaceborne?)…what would we do with it? Go to other planets? We couldn’t land the sucker, I’m thinking, so what then? Little exploration vehicle thingies?

Depends. If you’re talking a 4000-tonne Orion-sized monster, then I reckon you could afford the space for a landing vehicle or ten.

Well, both the British and theoreical physicists have tendencies towards ironic understandment, so no great surprise there. However, I’ve been thinking about this and I don’t see any great problems with what they’re proposing, provided they can get the pellets to detonate in the first place and can control the plasma thereafter. The yield per explosion is only 5 tonnes of TNT, after all. The main engineering problems with Orion were things like radiation shielding and the plasma ablating the pusher plate. I don’t see the shielding as that much of a problem in this case. And in this design the plasma is effectively pushing against some confinement field rather than steel, so you should avoid the latter. At the expense of all sorts of plasma physics headaches, no doubt.
It’s perhaps worth noting that similar schemes have been proposed before, though usually using fusion rather than fission. The best known is probably the British Interplanetary Society’s Daedalus project

Well, both the British and theoreical physicists have tendencies towards ironic understandment, so no great surprise there. However, I’ve been thinking about this and I don’t see any great problems with what they’re proposing, provided they can get the pellets to detonate in the first place and can control the plasma thereafter. The yield per explosion is only 5 tonnes of TNT, after all. The main engineering problems with Orion were things like radiation shielding and the plasma ablating the pusher plate. I don’t see the shielding as that much of a problem in this case. And in this design the plasma is effectively pushing against some confinement field rather than steel, so you should avoid the latter. At the expense of all sorts of plasma physics headaches, no doubt.
It’s perhaps worth noting that similar schemes have been proposed before, though usually using fusion rather than fission. The best known is probably the British Interplanetary Society’s Daedalus project, in which the pellets were to be bombarded by electron beams. Another example.

This is Johndale Solem’s idea. While the “small” explosions were more Orion-scaled than the 5 tonne ones, the general idea was to go for a smaller, zippier craft than Orion. When I heard him give a talk on the subject about 10 years back, his biggest worry seemed to be the bombs getting jammed in the ejection mechanism, which struck me as one of the lesser engineering problems involved.