Mystery with the GFI solved... I called Luhr Jensen today to talk to them about the problem. The lady on the phone told me that it's fairly common for the element to get some moisture trapped in it and instructed me to remove the element and put it in my oven at 250 degrees for an hour. She said that that should fix things up and if it didn't said that she'd send me a new element.

Since I had already used the smoker for six hours yesterday in a non-GFI socket, I figured that the element was probably void of any moisture. I came home and tried the GFI plug again and viola, everything worked as expected!