I'll bet that quite a few permits were required for that, even back then. Today, such a device would be unthinkable. It doesn't take much to irradiate the whole neighborhood.
Yes, I'm sure there are a lot of federal, state and local agencies that would have something to say about it. The NRC would probably regulate both the operation of the reactor and access to the enriched uranium fuel. Then there are the various environmental agencies. And of course you'd want to check with your friendly insurance agent to make sure your homeowner's policy covers the occasional nuclear mishap!
Actually, on another list it was pointed out that the LR reactor design is quite safe, because if it overheats, vapor bubbles will form in the fuel solution, which reduce its density and slow the reaction.
Check out this article about an engineer in Alaska who wants in install a cyclotron in his home, to produce radioisotopes for medical diagnostics:
http://www.wired.com/politics/law/news/2005/12/69726