Improvements in large language models have led to increasing optimism that they can serve as reliable evaluators of natural language generation outputs. In this paper, we challenge this optimism by thoroughly re-evaluating five state-of-the-art factuality metrics on a collection of 11 datasets for summarization, retrieval-augmented generation, and question answering. We find that these evaluators are inconsistent with each other and often misestimate system-level performance, both of which can lead to a variety of pitfalls. We further show that these metrics exhibit biases against highly paraphrased outputs and outputs that draw upon faraway parts of the source documents. We urge users of these factuality metrics to proceed with caution and manually validate the reliability of these metrics in their domain of interest before proceeding.