Pull down resistor not pulling current down to 0 V? - Arduino + LED's
The pull down resistor is in the wrong position, it should be on the output of the PWM pins. 

You only need them to keep the LEDs off when the Arduino is off or if the Arduino pins are set to the INPUT state. This is the default startup of the Arduino which is probably why you are seeing the LEDs coming on faintly. Either move the resistors to the PWM outputs or change the code to set the pins to OUTPUT.

By the way, what FET are you using?