In response to the various errors in handling chainsaws, whether running or not, here are some things to consider to change bad habits.
Before moving from a cut in a log or tree immediately hit the brake to stop the chain. When walking any distance engage the chainbrake and put the saw in your left hand with the bar/chain facing behind you. Put a scabbard on the chain and bar to further prevent injury if one trips, falls, etc.
Also, engage the chainbrake whenever starting the saw and release it once the saw begins to run. The brake may wear out slightly earlier than it would have otherwise, BUT if it keeps one from getting cut it's well worth the effort. On average a chainsaw chain moves at 88 feet per second, = 55-60MPH. There is no way to avoid the teeth at those speeds, UNLESS one catches the teeth in the chaps, which slows the momentum of the chain and reduces or eliminates the potential cut/damage.