Although you hear about the weird and strict rules in the media, most people will be fine in Dubai. Some prescription drugs along with illicit drugs are banned. While they might not search your medication, if they find codeine or valium etc on your person, you can be sent to jail for 3 years with no trial. If you are under the influence of such drugs, it’s the same thing. But I have been with people who have carried painkillers through with no issues. Usually people who are flagged for such issues have caused problems and have been rude/abusive for some other reason. Most of the time customs is fine.
You can’t bring pornography into the country. You can’t be drunk in public, however there are plenty of nightclubs and people on pub crawls, so it’s just a matter of not being a nuisance. Some buildings and places aren’t allowed to be photographed, and you have to be careful taking photos of locals (I have in the past, but had to be subtle). Dress standards are basic, women and men should cover their knees, women should usually cover their shoulders. But all it takes is a trip to the beach or the mall and a few Russian 20-something year old tourists before you realise these rules are rarely enforced.
All that aside, the UAE was recently declared as the second safest country in the world after Finland. Pickpockets and thievery are unheard of, and it’s warmer than Finland.