In modern electronic manufacturing, defect detection on Printed Circuit Boards (PCBs) plays a critical role in ensuring product yield and maintaining the reliability of downstream assembly processes. However, existing methods often suffer from limited feature representation, computational redundancy, and insufficient availability of high-quality training data -- challenges that hinder their ability to meet industrial demands for both accuracy and efficiency. To address these limitations, we propose MRC-DETR, a novel and efficient detection framework tailored for bare PCB defect inspection, built upon the foundation of RT-DETR. Firstly, to enhance feature representation capability, we design a Multi-Residual Directional Coupled Block (MRDCB). This module improves channel-wise feature interaction through a multi-residual structure. Moreover, a cross-spatial learning strategy is integrated to capture fine-grained pixel-level relationships, further enriching the representational power of the extracted features. Secondly, to reduce computational redundancy caused by inefficient cross-layer information fusion, we introduce an Adaptive Screening Pyramid Network (ASPN). This component dynamically filters and aggregates salient low-level features, selectively fusing them with high-level semantic features. By focusing on informative regions and suppressing redundant computations, ASPN significantly improves both efficiency and detection accuracy. Finally, to tackle the issue of insufficient training data, particularly in the context of bare PCBs, we construct a new, high-quality dataset that fills a critical gap in current public resources. Our dataset not only supports the training and evaluation of our proposed framework but also serves as a valuable benchmark for future research in this domain.