Safety is a topic not taken seriously enough in fly fishing. Fishing is by nature a water sport (no surprise there) and as such there are always risks.
Flies whizzing past your head increases the risk factor. And there are other dangers.
The dangers to be avoided are:
Drowning. I heard somewhere that forty anglers die each year in the UK from drowning. Learning to swim is a pretty good plus point here. Wearing bouyancy aids helps too, but best of all are self inflating braces. If you fall in and bash your head in the process the self inflating nature of these things will turn you around, keep your head above water and save your life. Expensive they may be - but what value your life?
Waistcoats with an integrated life preserver are a waste of money BTW - On a hot day you unzip them and then they won't operate correctly.
Hooking yourself and others. The loss of an eye is possible, no matter how good a caster you are. Always wear sunglasses. For night fishing I'd recommend wearing clear lenses. A hat helps immensely too. Get into the habit of always checking your backcast for stray humans. When in boats never cast over your boat partner's head. Also try to avoid casting at the same time.
Soft mud and slippery damns: absolutely treacherous. Take great care and carry spare clothes in the car.
Electrocution. Carbon rods are great conductors of electricity. Never cast near powerlines - look for them, they are not always signposted (although in England they are legally supposed to be). Electric storms are very dangerous too - unfortunately the fishing can be rather good - only you can judge the risk. Personally, I avoid fishing during them.
Getting lost - that M25 can be a bitch. Tell someone where you are going and make sure that they know you have returned.
Weils disease is carried by rats and spread through their urine, it enters cuts in the skin. If you come down with flu-like symptoms within three weeks of fishing, go see the doctor and tell him you have been fishing and what to look for.
Tetanus is also a killer. Get immunised.
Blue-green algae can be poisonous to touch. Avoid contact.
Hypothermia through cold and inadequate clothing can be a problem, especially in remote places - take plenty of warm clothes and drinks.
Heat stroke and sunburn are unpleasant to say the least - keep covered and wear a wide-brimmed hat.
Stranded afloat! In boats check the condition of the boat before leaving, make sure that there is plenty of fuel, spare oars and life jackets.
When travelling with the flyrod other, more exotic, dangers are encountered, such as bears, snakes, crocodiles and poisonous spiders. Find out what to expect and the skills needed to protect yourself.