I think one of the tricks to intarsia is twisting the yarn when you change colors. That way, you won't get holes and the different colors will be connected to each other. The video is good but if it doesn't help, try Googling intarsia video and see if one of the many others helps. You could also try just a simple swatch with two colors to work out the technique.
You also might simplify the eye design so that there's just black and white, not so many color changes.