Having done a couple of stopovers in Dubai I have a bit of experience.Two things that come quickly to mind for a short stopover are the Mall of Dubai and an afternoon/evening of "dune bashing".Dubai is a city so intense that 24 hours is only long enough to get a very quick taste...IMO.
The Mall of Dubai is interesting for many reason,one of which is the valet parking area which is located right at the front entrance. Bugattis, Ferraris and Rolls Royces lined up,one after the other.The one time I encountered a Bugatti Veyron Vittess was at that very place.Dune bashing? Just look it up on youtube. Fascinating and fun to say the least!