HELP! Hairdresser dyed my hair grey instead of blond

You said "cool, light blonde" - do you know what cool colours are?

The reason your hair is that colour is because you essentially directed them to dye your hair platinum blonde, and they obliged.

It's probably best next time to take a colour picture with you (or maybe don't use arbitrary qualifiers like "cool" in a design environment where it has a very specific meaning)

Also regarding the social media promotion they were doing, typically the management will determine what gets posted. If the hairdresser thought it looked good and presented it to the manager to be put up, and the manager/soc med team disagreed, it won't go up.

I did show them pictures. Most of my hair is the colour I wanted, it is just the hair on the side of my face that is a different colour.

Well if you showed them pictures of one thing and said another, they may well have tried to do both at once to keep you happy since that was basically what you were asking. Again, I think this is largely due to confusing information you gave them. Obviously if you don't like it, go see what can be done, there or elsewhere, but in general hairdressers do not make mistakes.

Any colourist is going to be pretty well versed with the chemicals and processes involved in colouring hair, and they aren't going to make rookie mistakes that someone using e.g. a home-dye kit in their shower might. While it's easy to think of them as unskilled workers, there is actually a signifcant requirement of both classroom and on the job learning required to even be allowed to do basic styling. There is virtually no chance it was a "mistake" on their part.