In Back to the Future when Marty goes back to 1955, he buys a Pepsi with the money in his pocket-where did he get 50s money?
Realistically though waiters don't examine every coin that's handed to them. As long as it's clearly a dime or whatever and not obviously visibly foreign, you're not going to do more than glance at it without paying attention. Marty could easily have paid with an 1980s coin without a tired, bored waiter noticing, because why would you scrutinise a coin that closely?
The question then is what happened to the coin after that, and how long did it remain in circulation before coming to the attention of the banking and broader authorities. Did it just circulate for decades without anyone noticing, or did it eventually get paid into a bank and flagged somehow? Would a bank clerk in the 1950s have noticed the date on a coin?
The flipside is that BTTF takes place in a world where time travel is possible, and probably not even that hard if one not especially renowned scientist with few resources can invent a time machine by himself. We presume Doc's the only person who ever discovered time travel because the film series presents it as such, but logically - if you consider how many gifted scientists there are in the world - he probably was not the only one. Governments and private bodies would plough billions into time travel if such technology was possible, and it clearly is possible within the physics of the BTTF universe.
Ergo, BTTF likely takes place in a world where other time travellers exist, they're just never mentioned onscreen as neither Doc or Marty ever encounter them. There may well be an entire X-Files style department dedicated to finding an neutralising OOT and OOP anomalies like an 1980s coin appearing in the 1950s.