Step 1: Understanding the Question:
We need to find the grammatical error in the given sentence. This type of question tests subject-verb agreement.
Step 2: Detailed Explanation:
The subject of the sentence is "Neither of the two candidates".
Words like 'neither', 'either', 'each', 'everyone', and 'anyone' are singular pronouns and require a singular verb.
The phrase "Neither of..." means "not the one and not the other," which is conceptually singular.
The verb used in the sentence is "have submitted". "Have" is a plural verb. The correct singular form is "has".
Therefore, the sentence should be: "Neither of the two candidates has submitted their application yet."
The error lies in the part "have submitted".
Note on 'their': While traditionally 'his or her' would be used, 'their' is now widely accepted as a singular pronoun in modern English to avoid gender-specific language. The most definitive error is the verb.
Step 3: Final Answer:
The error is in the phrase "have submitted". It should be "has submitted".