We present multicolor optical observations of the nearby (z=0.1685) gamma-ray burst GRB 030329 obtained with the same instrumentation over a time period of 6 hours, for a total of an unprecedented 475 quasi-simultaneous BVR observations. The achromatic steepening in the optical, which occurs at t~0.7 days, provides evidence for a dynamic transition of the source and can be most readily explained by models in which the GRB ejecta are collimated into a jet. Since the current state-of-the-art modeling of GRB jets is still fraught with uncertainties, we use these data to critically assess some classes of models that have been proposed in the literature. The data, especially the smooth decline rate seen in the optical afterglow, are consistent with a model in which GRB 030329 was a homogeneous, sharp-edged jet, viewed near its edge interacting with a uniform external medium or viewed near its symmetry axis with a stratified wind-like external environment. The lack of short-timescale fluctuations in the optical afterglow flux down to the 0.5% level puts stringent constraints on possible small-scale angular inhomogeneities within the jet or fluctuations in the external density.