How do I fix a leaky spigot on a rain barrel?
I don't think the threads have enough to make a water tight seal against the rain barrel. Teflon tape is good when you have many threads making a connection between two joints. Instead, I'd make the hole larger, put a nut, washer, and rubber gasket on each side with the rain barrel in the middle so you can compress the rubber washer against the rain barrel for a water tight seal. Here is it in the ever so descriptive ascii art:

            *
        ||| * |||  
| +-----+++---+++--
+-+     |||   |||       
| | +---+++---+++--
  | |   ||| * |||
  ^^^       *  ^
faucet   ^  ^  +--- gasket, washer, nut
         |  +-- rain barrel
         +-- nut, washer, gasket