The intensity and the phase of ultrashort pulses from a self-mode-locked Ti:sapphire laser operating in the vicinity of zero group-delay dispersion (GDD) have been completely characterized by the technique of frequency-resolved optical gating (FROG). For small values of negative GDD, the appearance of a dispersive wave in the pulse spectrum is manifested in the measured FROG trace, and pulse retrieval directly shows its association with a broad leading-edge pedestal. For positive GDD, we confirm previous experimental observations of picosecond pulses with large positive chirp and report a new operating regime in which the output pulses are of picosecond duration but are intensity modulated at 20 THz. The physical origin of this modulation is discussed by analogy with similar effects observed during pulse propagation in optical fibers, and the experimental results are compared with a model of intracavity four-wave mixing about the cavity zero GDD wavelength.