There might be some residual current leaking from the led pin on the arduino depending on how you have the pin set up in code.
Make sure you have
pinMode(ledpin,OUTPUT); //7 8 9 in the example circuit.
in your setup function - change out ledpin with whatever your pins are, you could even just use the numbers.
Also, likewise you may need a pulldown resistor from the pin directly to ground to make sure the capacitor in the mosfet doesn't cause you any trouble. Try adding a 10k resistor from each led output pin directly to ground. This higher value resistor will make sure the output truly sees 0v ground, but when the pin turns on, the 5v will easily overpower that resistor and go to the mosfet gate.