Revealing mistake: When Chekhov falls on the aircraft carrier a cloud of dust flies up as if he's landed on a mat or soft cargo. When we see him on the floor it's concrete.
Revealing mistake: When the whales first swim past the now submerged Klingon Bird of Prey, if you look to the right where the water is supposed to meet the distant horizon, you can see an exposed edge to the 'horizon' as the water moves up and down. This is the edge of the pool they are in, and the exposed edge is the bottom of the painting of the sky behind them. (01:46:30)
Revealing mistake: When the ship crash lands in the water, and they open the hatch you will see a wall, looks like some piping. When they show the outside of the ship no such wall exists.
Revealing mistake: When Kirk and crew flee the hospital McCoy bumps a man with his leg in a plaster cast. Look closely at the cast - it is fitted over his PJ's leg like a boot, plaster casts are never fitted over clothing.
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