The commonly used methods to characterize ultrafast laser pulses, such as frequency-resolved optical gating (FROG) and dispersion scan (d-scan), face problems when they are used on pulses varying within the acquisition time or laser beam. Such chirp variation can be identified by a discrepancy between the measured FROG and d-scan traces and their reconstructed counterparts. Nevertheless, quantification of the instability from the experimental data is a more complex task. In this work, we evaluate the precision of chirp instability quantification based on three different pulse characterization techniques. Two commonly used techniques FROG and d-scan are compared to a new method dispersion scan FROG (D-FROG) that combines the idea of dispersion scanning with the FROG method. We demonstrate the characterization of pulses generated from NOPA together with pulses processed by a 4f-pulse shaper without and with SLM-adjusted phase. In this paper, we validate the performance of the new method to estimate the chirp instability and, therefore, to improve the reconstruction of the measured results. Furthermore, we discuss the instability origin of each measurement case by using fast-scan autocorrelation traces.