To study the quality of thin metal/ZnO Schottky contacts (SCs), temperature-dependent current-voltage (I-V), capacitance-voltage, deep level transient spectroscopy, and photoluminescence measurements were performed using bulk, vapor-phase ZnO, treated by remote oxygen plasma (ROP). Au/ZnO and Pd/ZnO contacts on both O and Zn faces are compared as a function of the ROP processing sequence and duration. We find that (i) as the duration of ROP treatment increases from 2 to 4 h, Au/ZnO contacts on the Zn face, deposited before ROP treatment, become rectifying, while those on the O face remain Ohmic; (ii) with long-term ROP treatments prior to metallization, both Au/ZnO and Pd/ZnO show high-quality SCs; however, their I-V characteristics can be significantly degraded by electric field and high temperatures; (iii) ROP treatment can cause more H removal on the Zn face than on the O face, resulting in a decrease in the near-surface carrier concentration for the Zn face only; (iv) in addition to the dominant bulk-trap E3, surface traps, E6/E7 and E8, and Es, can be observed in Au/ZnO and Pd/ZnO SCs, respectively, on the Zn face, with shorter ROP treatment; and (v) with long-term ROP treatment, E3 (or L2) significantly increases and shifts in Au/ZnO SCs on the Zn face.