Answer:
Some actors work as a waiter until their big break.
Explanation:
The sentence that contains an inappropriate shift in person is the last one. Instead of <em>a waiter,</em> we should say <em>waiters </em>(<em>Some actors work as waiters</em>...). <em>Actors </em>is a plural noun and it should be followed by a plural noun. Another thing that confirms this is the use of the plural possessive pronoun <em>their</em>.
The rest of the sentences are correct. In the first sentence, there is no dilemma. In the second sentence, we have the phrase <em>many people</em>, which requires a plural verb and plural possessive pronoun. These conditions are fulfilled. The third sentence is a bit tricky because of the correlative conjunction <em>neither... nor.</em> The verb and possessive pronoun should be in the singular form in this case (as <em>Dave</em> is a singular noun), and they are, which makes this sentence correct.
This is why the fourth option is the correct answer.
