Advice to Tourists in OmanEdit This
If you follow these guidelines, you should encounter no difficulties of any kind:
Do not wear shorts or sleeveless blouses in public unless you are at the beach. Even there, do not wear two-piece bathing suits. The only exception to this is at a five-star resort on its private beach -- if it has one. Don't wear excessive amounts of make-up, and be relatively circumspect in your approach to local men. Steady eye-contact and broad smiles are highly unwise and may lead to unpleasant encounters.
It is not wise to wear shorts in public unless you are at the beach or are participating in some kind of sporting activity which justifies them. In sophisticated parts of the Capital Area -- Qurum, Al-Khuwair, or Medinat Qaboos -- it's okay. Outside of those up-market areas, it's not the best idea. That said, you won't be arrested or deported; however, someone may tell you to "dress properly." Short-sleeved shirts and tee-shirts are permissible, but tank-tops are not.
With few exceptions, non-Muslims are not encouraged to enter mosques in the Gulf. I have lived in the region since 1982 and have never been inside one, the one exception being a tour of the spectacular, new Sultan Qaboos Mosque which is now open to visitors.