Generative AI offers new opportunities for individualized and adaptive learning, e.g., through large language model (LLM)-based feedback systems. While LLMs can produce effective feedback for relatively straightforward conceptual tasks, delivering high-quality feedback for tasks that require advanced domain expertise, such as physics problem solving, remains a substantial challenge. This study presents the design of an LLM-based feedback system for physics problem solving grounded in evidence-centered design (ECD) and evaluates its performance within the German Physics Olympiad. Participants assessed the usefulness and accuracy of the generated feedback, which was generally perceived as useful and highly accurate. However, an in-depth analysis revealed that the feedback contained errors in 20% of cases; errors that often went unnoticed by the students. We discuss the risks associated with uncritical reliance on LLM-based feedback and outline potential directions for generating more adaptive and reliable LLM-based feedback in the future.