The NFPA says the dangers that exist when deep frying a turkey include:

Hot oil may splash or spill during the cooking. Contact between hot oil and skin could result in serious injury.
A hot oil spill can happen with fryers designed for outdoor use using a stand. The fryer could tip over or collapse causing the hot oil to spill. Newer countertop units using a solid base appear to reduce this risk. NFPA does not believe the risks of either type of turkey fryer to be acceptable because of the large amount of hot oil involved and the speed and severity of burns.
In deep frying, oil is heated to temperatures of 350° Fahrenheit or more. Cooking oil is combustible. If it is heated above its cooking temperature, its vapors can ignite.
Propane-fired turkey fryers must be used outdoors. They are very popular for Thanksgiving. Many parts of the country may have rain or snow at this time of year. If rain or snow hits the hot cooking oil, the oil may splatter or turn to steam, leading to burns.
Turkeys must be completely thawed before placing in the fryer, because a partially thawed turkey will cause the oil to splatter causing serious burns.
The fryers use a lot of oil, about five gallons. Considering the size and weight of the turkey, extreme caution must be taken when placing and removing the turkey from the fryer to be sure its is not dropped back into the fryer, splattering the oil on the chef. Happy Thanksgiving from the officers and members from Malvern Fire Company.