Stereoscopic, head-tracked display systems can show users realistic, world-locked virtual objects and environments. However, discrepancies between the rendering pipeline and physical viewing conditions can lead to perceived instability in the rendered content resulting in reduced immersion and, potentially, visually-induced motion sickness. Precise requirements to achieve perceptually stable world-locked rendering (WLR) are unknown due to the challenge of constructing a wide field of view, distortion-free display with highly accurate head and eye tracking. We present a system capable of rendering virtual objects over real-world references without perceivable drift under such constraints. This platform is used to study acceptable errors in render camera position for WLR in augmented and virtual reality scenarios, where we find an order of magnitude difference in perceptual sensitivity. We conclude with an analytic model which examines changes to apparent depth and visual direction in response to camera displacement errors.