If there is, then, whether the term is a common or a proper noun?
There were some instances of a single inconsistent spelling of a proper noun where it appears more than once.
On the other slip of paper he writes a word, either a common or proper noun.
Thus "John Smith" (particular; proper noun) and "Man" (general; common noun).
Is the following word "united" then, in this place, part of a proper noun, or merely an adjective?
A proper noun often consists of a group of words, some of which are perhaps ordinarily used as other parts of speech.
A proper noun becomes a common noun when used as a name that may be applied to any one of a class of objects.
A common noun becomes a proper noun when used as the particular name of a ship, a newspaper, an animal, etc.
The name of anything personified is regarded as a proper noun and is usually written with a capital letter.
Frank is a proper noun of the masculine gender, in the singular number and third person.