Looks like my problem was due to a shoddy soldering job. It looks like the drain and source on the mosfet were sporadically shorting out allow the current to flow to the relay. I cleaned up the spacing between the connections and it's been running trouble free now.
I thought my soldering iron was too hot, even at the lowest level, as I was having a hard time keeping the solder on the tip. Turns out the temp control potentiometer isn't doing anything and is sending full power to the iron. Guess I know what my next project is!