Disconect Battery

Nothing - if you're disconnecting for the winter, have it fully charged to prevent freezing . Disconnect the negative side first and connect it last any time working on a battery. It prevents shorting a metal wrench on something when removing the positive terminal. Disconnecting the battery sometimes clears codes in the ECU.

in a 2003 BMW if you completely disconnect the batter for a long period of time it will erase the user memory, your car does have cpu's in the car that know how you drive (i forget the term that is used specifically) but it will have to relearn your driving habits which gives you the most optimized gas mileage based off you as the driver... along with that you will lose your radio settings and what not as Tom mentioned above. Nothing that wont correct itself over time (cept maybe your clock and radio presets).