We search the archival Zwicky Transient Facility public survey for rapidly evolving transient (RET) candidates based on well-defined criteria between 2018 May and 2021 December. The search yielded 19 bona fide RET candidates, corresponding to a discovery rate of ∼5.2 events per year. Even with a Galactic latitude cut of 20°, eight of the 19 events (∼42%) are Galactic, including one with a light-curve shape closely resembling that of the GW170817 kilonova (KN). An additional event is a nova in M31. Four out of the 19 events (∼21%) are confirmed extragalactic RETs (one confirmed here for the first time) and the origin of six additional events cannot be determined. We did not find any extragalactic events resembling the GW170817 KN, from which we obtain an upper limit on the volumetric rate of GW170817-like KNe of R ≤ 2400 Gpc−3 yr−1 (95% confidence). These results can be used for quantifying contaminants to RET searches in transient alert streams, specifically when searching for KNe independently of gravitational-wave and gamma-ray-burst triggers.