apparently medical procedures are extremely cheap as well as electronics - like a hair transplant for £400 or a dvd and sat nav head unit for your car for £200
Consumer electronics are around the same price. In my multiple trips to Dubai i've never found anything worth buying where the price difference is enough to make transporting the thing home worthwhile. Mobile Phones are the only thing that have a substantial difference in price, and that's only really in that big french supermarket in The Mall of Emirates.
Medical Procedures, well it's all private so i'd imagine you get some lovely cheap little places up in Sharjah or somewhere. Cant say i'd like to use them though. They have a world leading hospital for cancer treatment though headed by Dr Rizyk, where my sister was treated for almost 2 years. Wouldnt say it was cheap though

The only real area where prices will surprise you is food. You can eat for very little money. Since you're only going for a day, and i'm assuming you dont want to spend a fortunre, i'd reccomend Shazzam in the MoE. You can look left and watch all *** chefs in the middle of the restaurant cooking your food, or look right and watch people snowboarding on the indoor ski slope (which, inciedntally, is awesome, and not very expensive)