Ockham's Spoon

My first thought on neutronium weapons was ultra-dense projectiles. Basically higher power versions of depleted uranium bullets. That removes a lot of the "weapon is too heavy to lift or swing" problems since the bullets are relatively small (although they still couldn't be made out of pure neutrons for reasons already mentioned) and the power comes from the gun. This would be especially appropriate for a weapon mounted on a vehicle or a mech.

I love raisins, and would take an oatmeal raisin cookie over a chocolate chip one any day, but the little girl's expression here is priceless

As noted above, involve the law so that it suits your play style, as intrusive or lenient as you want. But note that you can use the law to steer players away from scenarios you would like to avoid - e.g. maybe supers can be fined for property damage that occurs during fights which will make your heroes more careful during battles which might handicap them against villains who don't care. This also allows for good role-playing conflicts between supers who follow the law to the letter vs. those who want to stop the villains even if it means bending/breaking a few laws along the way. One note on Telepathy, if you don't want your team telepath solving mysteries too easily, having strict laws against mind reading can help keep their powers in check. Same for super-senses and other powers that can short-circuit some otherwise complicated plots.

This comes from Consumer Reports gaffe page of poor advertisements:

From Pat Byrnes:

I particularly like the fact that the diner is eating alone here