I think it might be a concern with foot/weight placement. On flats, (unless I'm wrong) I think the ball of your foot goes over the spindle, the center of your forefoot over the center of the pedal (think the way a mallet pedal looks) and you should get used to putting your weight *there*.

From there, you go to wearing clipless with the cleats on the shoes and lock-ins on the pedals (or in eggbeaters' case, just lock-ins) If there's a lot of slop and you feel like you're going to 'fall off' something might be maladjusted... OR maybe your midsole isn't rigid enough, lending to an unstable feeling?

Trying to get an idea of the problem...