i leave my car in sport all the time! i like to see the light in the dash light up. i believe the sport mode just covers the suspension to make it tighter and feel all the bumps in the road. i'll have to look in the manual when i get back from vacation!
If the dash depicts the 3/4 view drawing with just the engine/trans and steering wheel outlined then you are in Sport Mode, the shift points are raised and the steering is heavier. If you have an F-Sport or Luxury level of trim then you may then twist the Drive Mode **** a second time Clock-wise for Sport+ mode: the shocks will stiffen up as shown by the dash display now showing the struts as warandcar mentioned.
While the Eco Mode will remain engaged after a restart you must act to add Sport or Sport+ with every restart.