In electronics manufacturing, solder joint defects are a common problem affecting a variety of printed circuit board components. To identify and correct solder joint defects, the solder joints on a circuit board are typically inspected manually by trained human inspectors, which is a very time-consuming and error-prone process. To improve both inspection efficiency and accuracy, in this work we describe an explainable deep learning-based visual quality inspection system tailored for visual inspection of solder joints in electronics manufacturing environments. At the core of this system is an explainable solder joint defect identification system called SolderNet which we design and implement with trust and transparency in mind. While several challenges remain before the full system can be developed and deployed, this study presents important progress towards trustworthy visual inspection of solder joints in electronics manufacturing.