This is the pinout diagram from a Fairchild BS270 MOSFET datasheet.
I'm pretty sure that I know which pin is drain, but the jury's still out on the gate and source. What the heck were they thinking when they drew it this way?
I tried Ron's suggestion, and it showed that the source is at the end. Hence gate is the middle pin as Mickster and John said. Tested it in circuit, and it works correctly. So mystery solved. Thanks everyone.
I've been thinking about getting one of those gadgets, but wasn't sure how well they worked at identifying components. I guess I'll have to look into a bit more.