We provide the first full K2 transiting exoplanet sample, using photometry from Campaigns 1-8 and 10-18, derived through an entirely automated procedure. This homogeneous planet candidate catalog is crucial to perform a robust demographic analysis of transiting exoplanets with K2. We identify 747 unique planet candidates and 57 multiplanet systems. Of these candidates, 366 have not been previously identified, including one resonant multiplanet system and one system with two short-period gas giants. By automating the construction of this list, measurements of sample biases (completeness and reliability) can be quantified. We carried out a light-curve-level injection/recovery test of artificial transit signals and found a maximum completeness of 61%, a consequence of the significant detrending required for K2 data analysis. Through this operation we attained measurements of the detection efficiency as a function of signal strength, enabling future population analysis using this sample. We assessed the reliability of our planet sample by testing our vetting software EDI-Vetter against inverted transit-free light curves. We estimate that 91% of our planet candidates are real astrophysical signals, increasing up to 94% when limited to the FGKM dwarf stellar population. We also constrain the contamination rate from background eclipsing binaries to less than 5%. The presented catalog, along with the completeness and reliability measurements, enable robust exoplanet demographic studies to be carried out across the fields observed by the K2 mission for the first time.