We demonstrate full characterization of femtosecond pulse distortion induced by all-order polarization mode dispersion (PMD) at selected polarization states via second-harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements at an average power of under 28 nW. By applying the inverse of the measured spectral phase via a programmable pulse shaper, we compress the distorted pulses from more than 3 ps to nearly bandwidth-limited durations of less than 500 fs. Our results show that SHG FROG measurements performed by using fiber-pigtailed aperiodically poled lithium niobate waveguides can serve as a robust and sensitive tool for characterization of PMD-induced spectral phase.