Just an affidavit from court will solve the issue if problem arises. Father's name must be there in your ID. Same address must be there in your ID. He may execute an affidavit before a 1st class magistrate saying that you are his son and his name has been mis spelled in the documents.
In any document father's name is included for clarity only to ensure and differentiate between persons of the same name. Therefore, as long as your father;s name is correctly mentioned, although a small part by mistake omitted, it will not make any difference.
If all your documents have the same name of your father what has been given in one document then you don't have any problem.
If your father's documents shows that he has a middle name also then it is his own name and nothing to do with your name.
Wherever you are going to write your name, you are going to produce your documents/certificates alone and not your father's documents, hence there is no need to be panicked over your father's missing middle name.
No authority will be insisting you to produce your father's documents, hence be rest assured about it.