With the conclusion of the third observing run for Advanced LIGO/Virgo (O3), we present a detailed analysis of both triggered and serendipitous observations of 17 gravitational-wave (GW) events (7 triggered and 10 purely serendipitous) from the Searches After Gravitational-waves Using ARizona Observatories (SAGUARO) program. We searched a total of 4935 deg2 down to a median 5σ transient detection depth of 21.1 AB mag using the Mt. Lemmon 1.5 m telescope, the discovery engine for SAGUARO. In addition to triggered events within 24 hr, our transient search encompassed a time interval following GW events of <120 hr, providing observations on ∼1/2 of the events accessible to the Mt. Lemmon 1.5 m telescope. We covered 2.1%-86% of the LVC total probability (P total) for individual events, with a median P total ≈ 8% within <120 hr. Following improvements to our pipeline and the addition of serendipitous observations, we find a total of seven new optical candidates across five GW events, which we are unable to rule out after searching for additional information and comparing to kilonova models. Using both publicly available and our own late-time data, we investigated a total of 252 optical candidates for these 17 events, finding that only 65% were followed up in some capacity by the community. Of the total 252 candidates, we are able to rule out an additional 12 previously reported counterpart candidates. In light of these results, we discuss lessons learned from the SAGUARO GW counterpart search. We discuss how community coordination of observations and candidate follow-up, as well as the role of archival data, are crucial to improving the efficiency of follow-up efforts and preventing unnecessary duplication of effort with limited electromagnetic resources.