We qualitatively compared literature reviews produced with varying degrees of AI assistance. The same LLM, given the same corpus of 280 papers but different selections, produced dramatically different reviews, from mainstream and politically neutral to critical and post-colonial, though neither orientation was intended. LLM outputs always appear at first glance to be well written, well informed and thought out, but closer reading reveals gaps, biases and lack of depth. Our comparison of six versions shows a series of pitfalls and suggests precautions necessary when using AI assistance to make a literature review. Main issues are: (1) The bias of ignorance (you do not know what you do not get) in the selection of relevant papers. (2) Alignment and digital sycophancy: commercial AI models slavishly take you further in the direction they understand you give them, reinforcing biases. (3) Mainstreaming: because of their statistical nature, LLM productions tend to favor mainstream perspectives and content; in our case there was only 20% overlap between paper selections by humans and the LLM. (4) Limited capacity for creative restructuring, with vague and ambiguous statements. (5) Lack of critical perspective, coming from distant reading and political correctness. Most pitfalls can be addressed by prompting, but only if the user knows the domain well enough to detect them. There is a paradox: producing a good AI-assisted review requires expertise that comes from reading the literature, which is precisely what AI was meant to reduce. Overall, AI can improve the span and quality of the review, but the gain of time is not as massive as one would expect, and a press-button strategy leaving AI to do the work is a recipe for disaster. We conclude with recommendations for those who write, or assess, such LLM-augmented reviews.