Assessment is an essential part of education, both for teachers who assess their students as well as learners who may evaluate themselves. Multiple-choice questions (MCQ) are one of the most popular types of knowledge assessment, e.g., in medical education, as they can be automatically graded and can cover a wide range of learning items. However, the creation of high-quality MCQ items is a time-consuming task. The recent advent of Large Language Models (LLM), such as Generative Pre-trained Transformer (GPT), caused a new momentum for automatic question generation solutions. Still, evaluating generated questions according to the best practices for MCQ item writing is needed to ensure docimological quality. In this article, we propose an analysis of the quality of LLM-generated MCQs. We employ zero-shot approaches in two domains, namely computer science and medicine. In the former, we make use of 3 GPT-based services to generate MCQs. In the latter, we developed a plugin for the Moodle learning management system that generates MCQs based on learning material. We compare the generated MCQs against common multiple-choice item writing guidelines. Among the major challenges, we determined that while LLMs are certainly useful in generating MCQs more efficiently, they sometimes create broad items with ambiguous keys or implausible distractors. Human oversight is also necessary to ensure instructional alignment between generated items and course contents. Finally, we propose solutions for AQG developers.