Theoretical nucleosynthetic yields from supernovae are sensitive to both the details of the progenitor star and the explosion calculation. We attempt to comprehensively identify the sources of uncertainties in these yields. In this paper we concentrate on the variations in yields from a single progenitor arising from common 1D methods of approximating a supernova explosion. Subsequent papers will examine 3D effects in the explosion and the progenitor, and trends in mass and composition. For the 1D explosions we find that both elemental and isotopic yields for Si and heavier elements are a sensitive function of explosion energy. Also, piston-driven and thermal bomb-type explosions have different yields for the same explosion energy. Yields derived from 1D explosions are nonunique.