Cutting out a hole

[micheus]

matt, it would be easier if you had first made the central piece (the white one) and then extruded the left/right side faces to create the badge - using all those faces/edges you would have. You just would need the cut along Y axis and bridge the faces to get the hole.

You should have noticed the rim near from where you extruded the badge are straight line (edge), but it should be curved as the rest of the rim.