Oh, here's how to prevent the worst drop of all, the parking lot drop.
When you're "pedaling" the bike around to get it backed up/pointed in the right direction/etc, using both feet, keep your weight on your feet. Don't try to sit on the bike and push with your feet. One grease spot and you're going down with the bike. Keep the bike upright with your arms, and plant each foot and make sure of your grip before you shift your weight. If you're on a slippery spot, you'll feel it and have a chance to find a new stepping spot before you've committed the mass of the bike moving in a direction that you can't support.
Doing it this way changes "ohsht new blinkers" into "ooh, damn that was close."