Step 1: Check Part A.
One of the most talented is correct. One serves as the singular grammatical subject here.
Step 2: Check Part B.
Students in the class has failed is correct because the verb has failed agrees with One, not students. The singular verb is properly used.
Step 3: Check Part C.
To qualify for the examination is a correct infinitive phrase. There is no error in any part of the sentence, so Part D, No error, is the correct answer.
\[ \boxed{\text{No error.}} \]