From many of the videos I've seen on YouTube it seems people don't take any safety measures other than hoping that nothing goes wrong. Loads of videos show them flying over crowds, streets and traffic.

Many weigh a couple of kilos or more and even from 10 metres that would hurt... I saw someone get their arm/shoulder broken on a Thai beach when a coconut fell on them... I'd say it is currently more luck than design that has prevented a well publicised injury or accident. The shame is that one persons actions could see the whole activity become highly regulated or even banned...