Large-scale generative models are shown to be useful for sampling meaningful candidate solutions, yet they often overlook task constraints and user preferences. Their full power is better harnessed when the models are coupled with external verifiers and the final solutions are derived iteratively or progressively according to the verification feedback. In the context of embodied AI, verification often solely involves assessing whether goal conditions specified in the instructions have been met. Nonetheless, for these agents to be seamlessly integrated into daily life, it is crucial to account for a broader range of constraints and preferences beyond bare task success (e.g., a robot should grasp bread with care to avoid significant deformations). However, given the unbounded scope of robot tasks, it is infeasible to construct scripted verifiers akin to those used for explicit-knowledge tasks like the game of Go and theorem proving. This begs the question: when no sound verifier is available, can we use large vision and language models (VLMs), which are approximately omniscient, as scalable Behavior Critics to catch undesirable robot behaviors in videos? To answer this, we first construct a benchmark that contains diverse cases of goal-reaching yet undesirable robot policies. Then, we comprehensively evaluate VLM critics to gain a deeper understanding of their strengths and failure modes. Based on the evaluation, we provide guidelines on how to effectively utilize VLM critiques and showcase a practical way to integrate the feedback into an iterative process of policy refinement. The dataset and codebase are released at: https://guansuns.github.io/pages/vlm-critic.