Multi-shot pulse-shape measurements of trains of ultrashort pulses with unstable pulse shapes are studied. Measurement techniques considered include spectral-phase interferometry for direct electric-field reconstruction (SPIDER), second harmonic generation frequency-resolved optical gating (FROG), polarization gate FROG, and cross-correlation FROG. An analytical calculation and simulations show that SPIDER cannot see unstable pulse-shape components and only measures the coherent artifact. Further, the presence of this instability cannot be distinguished from benign misalignment effects in SPIDER. FROG methods yield a better, although necessarily rough, estimate of the pulse shape and also indicate instability by exhibiting disagreement between measured and retrieved traces. Only good agreement between measured and retrieved FROG traces or 100% SPIDER fringe visibility guarantees a stable pulse train.