Fast switching of Power MOSFETs

fungus:
First you have to figure out what the problem is.

The problem is that the MOSFETs take more time than they should to turn on and off thus leds that should not light up do so.

fungus:
What are the capacitors for?

for exactly that
It looks to me like they might be keeping the LEDs lit up for a short time after your MOSFET switches off.

fungus:
Why do you write to the output ports multiple times?

Ignore it. It has no impact on my problem whatsoever