I've got a set of Shimano SPD-compatible pedals, and I've noticed that one pedal is very secure- that is, there's very little rotation around the axis that goes through the top of my foot and comes out the bottom (yaw, for the aviation-minded). If I rotate that foot in the cleat, it tends to meet some resistance, and then pop out. The other foot (my left) can rotate back and forth quite a bit, especially when I'm bearing down on the pedals (like during a climb) without my foot popping out of the cleat. It feels kind of like the cleat doesn't have a good "grip" on my foot...
Is this something that I can have adjusted at my LBS? Is the spring-loaded part in the back not grabbing my shoe or something? The pedal is definitely engaged- I can pull up on the pedal and get it to move (and I get a distinct "click" when I try to lock my foot in), but as I said, it doesn't feel as secure as the opposite one.
I am unfamiliar with Shimano pedals, but check whether: (i) there is a tightening mechanism on the pedal itself; (ii) the wear and positioning of your cleats; and (iii) whether the cleats' screws have been sufficiently tightened.
