Is "in common" a noun? Some dictionaries say adjective, but some (Longman) have a 2nd definition for "in common" as a noun.
First of all, it's a phrase, so it can't be a single part of speech. I think what you mean to ask is "is it a noun phrase," meaning a phrase that functions as a noun. For example "The bewildered dog" is a noun phrase.
"In common" is a participle phrase, which essentially function as adjectives. A good test is to take a sentence with a proper noun or a pronoun and try to replace the noun with your phrase. If you can think of sentence that works, then you probably have a Noun Phrase. (You can do the same for other types of phrases).