Advances in artificial intelligence (AI) for surgical quality assessment promise to democratize access to expertise, with applications in training, guidance, and accreditation. This study presents the SAGES Critical View of Safety (CVS) Challenge, the first AI competition organized by a surgical society, using the CVS in laparoscopic cholecystectomy, a universally recommended yet inconsistently performed safety step, as an exemplar of surgical quality assessment. A global collaboration across 54 institutions in 24 countries engaged hundreds of clinicians and engineers to curate 1,000 videos annotated by 20 surgical experts according to a consensus-validated protocol. The challenge addressed key barriers to real-world deployment in surgery, including achieving high performance, capturing uncertainty in subjective assessment, and ensuring robustness to clinical variability. To enable this scale of effort, we developed EndoGlacier, a framework for managing large, heterogeneous surgical video and multi-annotator workflows. Thirteen international teams participated, achieving up to a 17% relative gain in assessment performance, over 80% reduction in calibration error, and a 17% relative improvement in robustness over the state-of-the-art. Analysis of results highlighted methodological trends linked to model performance, providing guidance for future research toward robust, clinically deployable AI for surgical quality assessment.