Actually, a "mistake" can be either abstract or concrete.
"He must have made a mistake doing that math in his head because his
That's clearly abstract. The mistake is complete intangible and exists merely as an idea.
"Those four cupcakes are mistakes. You can eat the mistakes if you
like, but the ones that aren't mistakes are for company."
That's clearly not abstract because you can literally pick up and eat the mistakes.
As for "mistake" being a countable noun, which it is, that has absolutely nothing to do with whether or not it's abstract or concrete. Say a bunch of quarters are on a table. I can say, "The coins are on the table." I can say, "The money is on the table." In those sentences, "coin" is a count noun and concrete and "money" is a non-count noun and concrete. They're both concrete nouns as they both indicate the exact same tangible objects lying on the table, so being concrete doesn't preclude a noun from being non-count and being a count noun does't mean a noun is necessarily concrete, as the very first example sentence above demonstrates.