HD,
The UAE is, in my opinion, considerably safer than most European cities - certainly the fair few that I've visited. There are a few incidents that take place, but the amount of crime considering the population count is very low. People here leave bikes, etc, unsecured in car ports and they don't go missing. There is no 'nuisance youth' problem as there is back in the UK and the family don't feel at all intimidated strolling the streets at night.
In terms of political issues, the UAE is probably the most stable environment in the Middle East. There have been no visible protests (at least none that I've seen).
All in all it's a great place to live, although best to escape for the peak of the summer if possible.