If I was fired over a mistake that was made by someone else, what can I do?
Unfortunately, there probably is nothing you can do. You do not mention an employment contract or agreement. In the absence of such a contract or agreement, your employer may terminate your employment at any time, for any reason--and that includes for reasons which are unfair or which are founded on some factual mistake (for example, blaming you for something someone else did). It is unfortunately the case that without a contract, you have essentially no rights to or protection for your job.