Humans seamlessly fuse anticipatory planning with immediate feedback to perform successive mobile manipulation tasks without stopping, achieving both high efficiency and reliability. Replicating this fluid and reliable behavior in robots remains fundamentally challenging, not only due to conflicts between long-horizon planning and real-time reactivity, but also because excessively pursuing efficiency undermines reliability in uncertain environments: it impairs stable perception and the potential for compensation, while also increasing the risk of unintended contact. In this work, we present a unified framework that synergizes efficiency and reliability for continuous mobile manipulation. It features a reliability-aware trajectory planner that embeds essential elements for reliable execution into spatiotemporal optimization, generating efficient and reliability-promising global trajectories. It is coupled with a phase-dependent switching controller that seamlessly transitions between global trajectory tracking for efficiency and task-error compensation for reliability. We also investigate a hierarchical initialization that facilitates online replanning despite the complexity of long-horizon planning problems. Real-world evaluations demonstrate that our approach enables efficient and reliable completion of successive tasks under uncertainty (e.g., dynamic disturbances, perception and control errors). Moreover, the framework generalizes to tasks with diverse end-effector constraints. Compared with state-of-the-art baselines, our method consistently achieves the highest efficiency while improving the task success rate by 26.67\%--81.67\%. Comprehensive ablation studies further validate the contribution of each component. The source code will be released.