The effects of internal molecular fluctuations on chemical oscillations and chaos are investigated using a lattice-gas model for the dynamics of spatially distributed reacting systems. For limit cycle oscillations, the manner in which temporal correlations develop long-range order as the system size increases is studied. For chaotic attractors the correlation functions indicate the existence of noisy periodic behavior for global concentration variables. These features are explored for the three-variable autocatalator model. The effects of fluctuations on transverse front instabilities in the cubic autocatalysis reaction are also studied. The front instability is investigated in the lattice-gas model, and fluctuations are shown to lead to diffusive roughening of the front below the instability point and, in addition, to modify the cellular structure above the instability point.