1. Always change your money in official Exchange office.
2. 1 EUR is around 115 RSD. Serbian dinar is only official currency in Serbia, don't try to pay with foreign money. (More info here: Rates)
3. In Belgrade public transport is not free. You may buy tickets at almost any kiosk.
4. Bus ticket is double price in vehicles.
5. If you are satisfied with service you should probably tip the waiter (normal tip is 20-100 RSD).
6. Always use taxi with -TX suffix licence plates. Start is 170 RSD, and one kilometer is around 50-70 RSD. Always use taxis with radio connections.
7. Don't curse in English or in other mayor European language - locals probably will understand it.
8. Avoid conversation about Kosovo, Albania, and other political themes.
9. Prefer speech about customs, culture, history, night life, shopping, leisure etc.
10. Belgrade is safe city but there is a probability of pick-pocketing in over-crowded buses. Watch on your belongings.