The biggest one is that, well... The test doesn't aim to see what GPT-4 can do and how well it does it, only whether the participant can guess the (possibly cherry-picked) answer the author decided on. In short, we don't know if he sampled answers and decided on the most probable answer (akin to consensus voting/self-consistency[1]), or if he asked a question and chose the first one.
Maybe GPT-4 guesses the correct answer for a question 80% of the time, but he got unlucky? You don't know, the author doesn't tell you. The answers are generated ahead of time and are the same every time you go through the test.