The obvious danger is a large amount of super hot oil.
The key tip is to make sure you put your fryer on a flat surface that is outside. Do not fry it indoors.
Do not use a fryer on a wooden deck, or in the garage.
Make sure your turkey is completely thawed.
Never leave the fryer unattended and make sure you keep kids and pets away from it.
If it does catch on fire, do not use water to put it out. Keep a fire extinguisher handy.