As others have already explained, "validated parking" means that the shop or business "validates" your parking in some Pay By The Minute/Hour facility so you park for free. In the small city I live in the parking garages (multi-story parking structures) are owned and run by the city. When you enter you collect a ticket with a mag strip on it. If you patronize one of the businesses they will give you a ticket sized card. When you leave the parking structure you feed the toll gate your parking ticket and instead of feeding money into the toll gate you feed the business' card in and leave for free.
Prior to the widespread use of mag strips and computerized pay stations, the businesses would stamp your parking ticket and you would show that to the human attendant when you left.
As for the No Fare Bus scenes, some companies and transit authorities are experimenting with or installing RFD systems. (Like the FastTrak or other bridge/highway toll pre-pay setups that you can get for your car in many places.) As long as you have the credit card-sized, um, card, on you when you board, the bus' reader will automatically deduct the fare from your balance. But most likely it was just the director being lazy and saving some screen time by not showing the character dropping coins in the box.
