I agree that the error is obvious in the given example "One of my sisters' friend" because the one of
prepositional phrase requires an object that is plural in number.
Some people erroneously view the phrase "one of my sisters'" as a single individual and treats it as the possessive form that describes a noun, in this case, friend
My sister's/sisters' friend
My sister Barbara's friend
Those phrases are all easy to understand. When it comes to "one of," some speakers immediately substitute it with the possessive and think, "One of my sisters' [Barbara's] friend is in town," which is incorrect. For it to be grammatically correct, "one of" must refer to a plural possessed object "friends" rather than "sisters."
In sum, when one incorrectly identifies the object in the prepositional phrase "one of," then it becomes a problem.