Doin' good so far...'cept for the missing flyback diode always use one...make sure you get it in the right way!
Are you using an N-channel MOSFET? Using the PIC to add a ground to the coil? The 100k resistor is bleeding off any leakage coming thru the MOSFET. N-channel aren't so bad for this, P-channel's are worse (and you have to pull the gate the other way)...that's probably why the MOSFET would turn on for no apparent reason.