Large language model (LLM)-based judges are increasingly used to scale the evaluation and optimization of open-ended medical dialogue systems, making their reliability critical in this high-stakes setting. However, existing medical benchmarks mainly assess their medical knowledge, while general judge benchmarks lack clinically grounded consultation criteria. To address this gap, we introduce Med-GRADE, a benchmark for evaluating LLMs as medical dialogue judges. It contains 2,076 real-world patient–LLM dialogues annotated by 56 physicians with a 23-item rubric adapted from Mini-CEX, covering Medical Interviewing (MI), Humanistic Care (HC), and Diagnosis and Treatment Management (DTM). Experiments on 17 LLMs show that current LLM judges achieve only moderate agreement, with the best model reaching 64.89% Macro-F1 and 68.28% Hamming Accuracy. Besides, more complex prompts may even harm performance: CoT disrupts parsing, while few-shot and self-refine introduce item-level instability. Data and code are available at https://github.com/jyd777/Med-GRADE for reproducibility.