As for dress code, Dubai is very tolerant although officially a muslim country.
If you want to be a little bit respectful, long trousers & long sleeve for men, but shorts & polo are perfectly fine.
For ladies, the idea is to show as little skin as possible and to hide your silhouette, but, frankly, it's quite free.
As long as you are not visiting a religious place, wear anything that the morality of your country of origin tolerates.
Just keep in mind that inside malls can be very cold due to the combination of A/C and marble.
Avoid PDA : public displays of affection.
kq747 : I've never seen the morality police. I've seen something close in Iran and Saudi Arabia. But, AFAIK, it doesn't exist in Dubai. Otherwise, they would have plenty of work ...
