mistake是可数名词,只能说There must be some mistakes.Theremust be some mistake是错误的表达.
第二问：
我尝试用动词给你解答
I have reserved for a standard room/I have reserved a standard room.
名词：my reservation is for a standard room/my reservation is a standard room
不管是动词还是名词,都可以加for或者不加for
为什么?
因为reserve即可以做及物动词,又可以做不及物动词,不及物动词必须加介词接宾语
从reserve动词的用法你就能明白为什么名词形式里有for了
明白了吗?