Comments made during the public speaking section of the council's meeting are not agenda items so shouldn't be minuted verbatim. It is more usual for the minutes to read something like "a member of the public raised comments about X or Y" rather than include the comments in full. If any item raised in a public speaking section warrants further discussion, it should be an agenda item for a subsequent meeting. So, if your minutes are more detailed (whether the subject raised is correct or not), they should not be and secondly if there is a further comment to be made by the council or any one else on the points raised, then that should be an agenda item which can be minuted more fully at the subsequent meeting.
As has been said, you cannot add anything to the Minutes of a meeting which did not actually happen or was said, even if proposed at the subsequent meeting at which those minutes are agreed. Minutes are a record of what was agreed, not what you would have liked to have happened!