Approximate Computing (AxC) is increasingly becoming a new design paradigm for energy-efficient Integrated Circuits (ICs). Specifically, application resiliency allows a tradeoff between accuracy and efficiency (energy/area/performance). Therefore, in recent years, Error Metrics have been proposed to model and quantify such accuracy reduction. In addition, Error thresholds are usually provided for defining the maximum allowed accuracy reduction. From a testing point of view, Approximate Integrated Circuits offer several opportunities. Indeed, approximation allows one to individuate a subset of tolerable faults, which are classified according to the adopted threshold. Thanks to fewer required test vectors, one achieves test-cost reduction and improvements in yield. Therefore, using metrics based on the calculation of Mean Errors (ME metrics), has become a major testing challenge. In this paper, we present this problem and investigate the technical requirements necessary for ME metric testing. We perform experiments on arithmetic circuits to study opportunities and challenges in terms of complexity. Our results show that one can filter up to 21% of faults and also highlight the complexity of the problem in terms of execution-time.