Continuity mistake: Notice the candle on the table in the Italian restaurant scene during Capt. Kirk and Dr. Gillian dialog. It changes height depending who is talking. (01:03:50 - 01:08:30)
Other mistake: When Kirk uses his hand phaser to melt the lock on the door in the hospital operating room, the phaser is not pointed directly at the lock. The beam leaves the phaser at an angle, which is probably not how the phaser would have been designed to operate. (01:25:20)
Continuity mistake: In the operating room, when Kirk uses a phaser to melt the lock, the hand he is holding the phaser in switches hands in the closeup shot. Additionally, the arm holding the weapon in the closeup is no longer in hospital scrubs, but a similarly colored sweatshirt. (01:25:20)
Answer: The United Federation of Planets uses the credit. Its a purely electronic form of money. Necessities and luxuries both are simple and cheap to produce with the Federation's advanced technology, and humanity has matured to the point that accumulating wealth is considered vulgar. Furthering the common good or the advancement of humanity is the real status symbol in the 23rd and 24th century. These conditions result in a society with very little need for money. Citizens are paid, but since the technology built into a place of business (or starship) or home supplies all basic needs for free, most people spend money only on exotic products that aren't commonly manufactured, like art or handmade foods.
Grumpy Scot