Local fluctuations and fluctuation-induced transitions in catalytic CO oxidation are studied with field electron microscopy on the (112) facets of a [100]-oriented Pt field emitter tip. The reaction is investigated in the bistable range close to the cusp point (critical point) that terminates the bistability range in pCO, T-parameter space. The amplitude and the spatial coherence of the fluctuations increase on approaching the critical point. The fluctuations are spatially well correlated on each flat (112) facet, but their correlation decays rapidly across stepped regions that terminate the flat facets. On smaller (112) facets, an onset of fluctuation-induced transitions is observed earlier (i.e., further away from the critical point) than for larger (112) facets. The behavior of the reaction system near the cusp point appears to be similar to that of an equilibrium system near the critical point. The observed fluctuations are mimicked in a simple reaction model for CO oxidation on surfaces that incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen. The steady states of the model exhibit a cusp bifurcation, from a regime of bistability to one of monostability. The fluctuations increase near this cusp point, as in experiment. This behavior is analyzed via kinetic Monte Carlo simulations and analytic procedures, focusing on the consequences for fluctuation-induced transitions.