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Quality assurance is of great importance for deep learning (DL) systems, especially when they are applied in safety-critical applications. While quality issues of native DL applications have been extensively analyzed, the issues of JavaScript-based DL applications have never been systematically studied. Compared with native DL applications, JavaScript-based DL applications can run on major browsers, making the platform- and device-independent. Specifically, the quality of JavaScript-based DL applications depends on the 3 parts: the application, the third-party DL library used and the underlying DL framework (e.g., TensorFlow.js), called JavaScript-based DL system. In this paper, we conduct the first empirical study on the quality issues of JavaScript-based DL systems. Specifically, we collect and analyze 700 real-world faults from relevant GitHub repositories, including the official TensorFlow.js repository, 13 third-party DL libraries, and 58 JavaScript-based DL applications. To better understand the characteristics of these faults, we manually analyze and construct taxonomies for the fault symptoms, root causes, and fix patterns, respectively. Moreover, we also study the fault distributions of symptoms and root causes, in terms of the different stages of the development lifecycle, the 3-level architecture in the DL system, and the 4 major components of TensorFlow.js framework. Based on the results, we suggest actionable implications and research avenues that can potentially facilitate the development, testing, and debugging of JavaScript-based DL systems.