With the rise of text-to-image (T2I) generative AI models reaching wide audiences, it is critical to evaluate model robustness against non-obvious attacks to mitigate the generation of offensive images. By focusing on ``implicitly adversarial'' prompts (those that trigger T2I models to generate unsafe images for non-obvious reasons), we isolate a set of difficult safety issues that human creativity is well-suited to uncover. To this end, we built the Adversarial Nibbler Challenge, a red-teaming methodology for crowdsourcing a diverse set of implicitly adversarial prompts. We have assembled a suite of state-of-the-art T2I models, employed a simple user interface to identify and annotate harms, and engaged diverse populations to capture long-tail safety issues that may be overlooked in standard testing. The challenge is run in consecutive rounds to enable a sustained discovery and analysis of safety pitfalls in T2I models. In this paper, we present an in-depth account of our methodology, a systematic study of novel attack strategies and discussion of safety failures revealed by challenge participants. We also release a companion visualization tool for easy exploration and derivation of insights from the dataset. The first challenge round resulted in over 10k prompt-image pairs with machine annotations for safety. A subset of 1.5k samples contains rich human annotations of harm types and attack styles. We find that 14% of images that humans consider harmful are mislabeled as ``safe'' by machines. We have identified new attack strategies that highlight the complexity of ensuring T2I model robustness. Our findings emphasize the necessity of continual auditing and adaptation as new vulnerabilities emerge. We are confident that this work will enable proactive, iterative safety assessments and promote responsible development of T2I models.