It's something I haven't seen many people mention, probably because it becomes intuitive once you are fixed (someday you all will be... muah ha ha ha)
Just don't freakin lean when you turn. It's better for winter riding on ice too. Try to set your spin so that the pedal that's going to be on the inside of the turn is on the way up on your way through the turn. Put hard push back (nowhere near enough to skid) on that pedal as you go through the turn, preferably right as you want to hit the 90 degree mark (summer only, just slow down and stay vertical on ice). A quick, vertical turn is better for avoiding traffic too.
The nice thing about riding a track bike on the streets is that it's so much more responsive that you can go around the corners with just a flick of a wrist. You don't need to usually dip at all...
Most of the scars on my pedals are from trying to squeeze to the right of cars and running a pedal into the curb - there's not much you can do about that.
Anyone else ever look at video of motorcycle racers and wonder how they can hit those corners leaned over so far? I've seen some where they're pretty much horizontal to the road....