Single leg drills are probably the best for improving your spin. With both feet clipped in you can get by mashing the downstroke, but if you are only using 1 foot you can't cheat. It really helps build strength and endurance in the muscles that you use for the upward part of the stroke.
Another reason that you might be moving your front wheel around a lot is if your bike is a little long for you. If you are over reaching you'll have a tendancy to pull on the handlebars with each pedal stroke and it causes front wheel wobble.