In a true competitive Turing test, these reasoning pitfalls could be included in the system prompt, there are not that many of them. The tester would need to find a novel reasoning pitfall, but those aren't uncommon among humans either, so that would not make a very useful differentiator.
Another approach could be to probe the helpfulness of an AI. A human would likely not comply with a request to write a sonnet about tangerines.
Another approach could be to probe the helpfulness of an AI. A human would likely not comply with a request to write a sonnet about tangerines.