It would be awesome if in later stages of the game when game world would be more dynamic if we could impress other girls by running at top speed or picking up heavy weights

Love to see a leveling system. I know it's far off, but I'd like to see something like this:

Strength stat: Lift heavier objects as if they were lighter. Lifting unconscious characters will be easier, moving objects will require less effort. Some object not able to be previously moved/lifted now can be. Raised by training at the gym, lifting weights or by general labor work.

Speed stat: Increases movement speed. 'Nuff said. Raised by walking/running on the treadmill and general running around. Raises faster on the treadmill however.

Awareness/Perception stat: You can overhear conversations at greater distances, allowing you to eavesdrop and obtain useful information. Also enables a tip message when dealing with certain NPCs, allowing you to predict certain things (for example, working in a store, you it'll give you a tip on what the NPC would be looking for). Raised by misc quests to find little objects and such.

Charisma stat: You can more easily convince an NPC to do what you say. Can gain favor or forgiveness from NPCs for saying certain things. Allows you to slack off more at the workplace as your boss will accept your excuses more often. Raised by simply talking to NPCs.

Typically there's a fifth stat in here for Luck or something, but I don't see it working its way in, outside of randomly gaining extra cash or something.