Your answer would be that "watching a scary film with my friends at the theater" is a sentence fragment.
Explanation:
"Watching a scary film with my friends at the theater" is a sentence fragment. Sentece fragments are groups of words that look like sentence, but aren't. To be a sentence, groups of words need to have at least one independent clause. An independent clause is any group of words that contain both a subject and a verb and can stand on its own as a sentence because it represents a complete thought. In this case, the sentence fragment fails to stand on its own because it does not represent a complete thought. It contains neither a subject nor a predicate (see 1) as opposed to the other sentences which are independent clauses (2 & 3).
1) *Watching a scary film with my friends at the theater
2) Call me
3) If you do not understand, ask your teacher for help
"That was Adam and him at the library" and "<span>Our neighbors are them and the Smiths</span>" is correct. When in doubt just try seeing how these sentences sound without the added nouns "Adam" and "the Smiths".