We combine spectroscopic measurements of H\(\alpha\) and H\(\beta\) and UV continuum photometry for a sample of 676 galaxies from the MOSFIRE Deep Evolution Field survey to constrain hydrogen ionizing photon production efficiencies (\(\xi_{\rm ion}\), xi_ion) at z=1.4-2.6. We find average log(xi_ion/[Hz erg\(^{-1}\)])=25.06 (25.34), assuming the Calzetti (SMC) curve when correcting the UV emission for dust attenuation. We conclude that the large scatter of 0.28 dex in xi_ion cannot be solely explained by measurement uncertainties or variations in the assumed dust attenuation curve from object to object. Rather, our analysis suggests that the scatter in xi_ion is also affected by galaxy-to-galaxy variations in stellar population properties, including the slope and upper mass cutoff of the IMF, stellar metallicity, bursty star formation, and binary/single star evolution. Moreover, we find that xi_ion is elevated in galaxies with high ionization states (i.e., high [OIII]/[OII]) and low oxygen abundances (low [NII]/H\(\alpha\) and high [OIII]/H\(\beta\)). However, xi_ion does not correlate with the offset from the z~0 star-forming locus in the BPT diagram, suggesting no change in the hardness of ionizing radiation accompanying the offset from the z~0 sequence. We also find that the xi_ion of galaxies with blue UV spectral slopes (\(\beta\)~-2.1) is elevated by a factor of ~2 relative to the average xi_ion of the sample. If these blue galaxies are similar to those at z>6, our results suggest that a lower LyC escape fraction is required for galaxies to maintain reionization, compared to that previously assumed based on the canonical xi_ion predictions from stellar population models. We also demonstrate that even with robust, dust-corrected H\(\alpha\) measurements, the UV dust attenuation curve is an important source of uncertainty that on average causes ~0.3 dex systematic uncertainty in xi_ion measurements.