In respect of what you are asking, historically apart from the one isolated incident, now nearly 4 year ago, it is safer than any major city in the US or Europe. That goes for petty crime to major incidents.
On the wife front, she may feel a little uncomfortable if going alone to areas that are predominantly male (furniture souk, fruit and veg market, camel market etc), but general shopping and the major malls and supermarkets are absolutely fine.