Students said the error meant there were two possible correct answers to the multiple choice questions.
Officials have said they will accept two answers as correct in each case, and the head of the national exam board has offered to resign.
The annual test determines the academic futures of high school students.
South Korean media said the mistake would affect the test scores of about 3,600-4,000 students.
"I express deep regret and recognise an urgent need to improve the question-making process," Education Minister Hwang Woo-Yea said in a statement broadcast on television.
"We will investigate the root cause of the problem," Mr Hwang said.
About 640,000 students sat the nine-hour standardised test, called the College Scholastic Ability Test, on 13 November at 1,216 testing sites across the country, South Korea's Yonhap news agency said.
Many students engage in intense studying for years in preparation for the exam, often with the involvement of their parents in what is an extremely competitive academic environment.
A good score would mean a spot in one of South Korea's top universities.
The suspect multiple-choice questions, one in the biology exam and one in the English language paper, sparked an uproar with parents and students complaining to the website of the Korea Institute for Curriculum and Evaluation (KICE) which administers the exam.
Last year's exam was also controversial because of a mistake in one of the questions in the world geology section.
After a year-long legal battle, Seoul High Court ruled in favour of four students who said the question was flawed.
"We did our best this year to prevent erroneous questions... but again there were faulty questions, causing chaos and inconvenience among exam takers, their parents and teachers," said Kim Sung-Hoon, head of KICE.
South Korea's education minister has apologised after two faulty questions in the national college entrance exam left thousands of students confused.