Data from Phasor Measurement Units (PMUs) inform powerful diagnostic tools that can help avert catastrophic failures in the power grid. Because of this, PMU measurement errors are particularly problematic, and it is critical to understand their impact. However, there is limited understanding of how much the PMU measurement errors affect the performance of various synchrophasor-based applications, and thus the ability of these applications to fulfill the users' requirements effectively is also unclear. This paper examines internal and external factors contributing to PMU phase angle and frequency measurement errors. A generic method is proposed to evaluate the impact of measurement errors on application performance. The impact of measurement errors on several synchrophasor-based Wide Area Monitoring System (WAMS) applications are analyzed as examples. These applications include power system disturbance location, oscillation detection, islanding detection, and dynamic line rating. The analysis demonstrated that the proposed method can be used to quantify the measurement error impact and analyze the performance degradation of these applications due to the measurement error. It also reveals that the impact of measurement error depends on the type, algorithm, and parameters of applications.