Ok, Let's hold on a moment - You're all answering questions before you know all of the facts.
Let's see what we know so far:
It's an OS 61FX which is a 2-stroke.
The prop, washer and nut seem to be placed correctly.
What we don't know is:
When does it come off? Does it come off immediately as you're starting the engine, or does the engine start, run for a few seconds/minutes, and THEN come off?
ORIGINAL: Chickenhawk
The engine actually started backwards once!
This is not unusual at all. It happens when the engine has been primed too much.
ORIGINAL: Chickenhawk
It seems like these should be reverse threaded or the engines + props should turn in the other direction.
No, the thread is in the correct rotation. As the prop spins CCW (looking from front) it helps to keep the nut tight (Because the nut tightens CW). It's when an engine backfires that the engine tries to rotate CW that the nut will come loose because the prop and nut are spinning CCW so once the engine switches to running CW that momentum causes the prop and nut to spin off.