Check for proper tire pressure, if you're packing extra weight (saddle bags or backpack) add a extra lb. or two of air.
Also for the added weight, check shock adjustment (make stiffer) if you have adjustable shocks.
Check and lube chain, you may have to re-adjust for the added weight.
Check transmission oil (might as well replace it with new).
If your ped has a battery, check electrolyte level and terminal connections.
Check that all the lighting is functional, carry extra bulbs.
If riding at night, have something reflective on your backpack and helmet, and some clear glasses/goggles. Also a small flashlight in the tool bag.
Raingear and extra clothes in a waterproof bag.
If you're crossing state lines, check their moped laws.
Snack food, (powerbar, beef jerky, etc.) and a bottle of water.
A cable or chain with lock.
Water pistol filled with ammonia within reach (for them damn dogs).
Aspirin and sun block.
Cell phone and credit card.
Check in with loved ones occasionaly.