Has the sorting hat been wrong?
NO, sorting hat has never been wrong. As the sorting hat sorts students at the age of 11 their choices and traits may change in future. Sorting hat can never be wrong as it chooses students based on the traits they value not on the traits they posses.
What was the Sorting Hat mistakes?
Everyone makes mistakes, even magically enchanted hats. However, sometimes the Sorting Hat gets it wrong. When Neville Longbottom was being sorted, he begged to be put into Hufflepuff, but the Sorting Hat refused his wishes and placed him in Gryffindor. Of course, it turned out the Hat was right.