Charge transfer across organic-inorganic interfaces plays a vital role in many important applications. Dye-semiconductor systems are the prototypical such interface and provide an excellent platform for exploring the underlying molecular-level factors that affect charge transfer dynamics and efficiency. Experiments often show multi-exponential electron injection kinetics from adsorbed dyes to a semiconductor substrate, suggesting the presence of interfacial heterogeneity. Nonetheless, both the diversity of interfacial structures and the associated implications for electronic dynamics are poorly understood. In the present work, we examine the effect of structural heterogeneity and dynamics on charge injection (as measured by dye-semiconductor electronic coupling) from plane wave density functional theory and ab initio molecular dynamics calculations on model dye-semiconductor systems. We demonstrate that dye binding motif, conformation, solvation, and corresponding thermal fluctuations significantly affect charge injection kinetics. We suggest that the experimentally observed multi-exponential kinetics likely result not only from an intrinsic heterogeneous distribution of electronic coupling strengths, but also from the conformational or solvent dynamics that in turn modulate the coupling strength and/or band alignment.