Malaria rapid diagnostic tests (mRDTs) that detect histidine-rich protein 2 (HRP2) remain the mainstay of falciparum malaria diagnosis in Sub-Saharan Africa. Understanding their test characteristics when used for surveillance in asymptomatic populations is important. We explored the rate of false-positive and false-negative mRDT results among asymptomatic persons >5 years old screened for malaria at schools and clinics in the rural Bagamoyo District using 18S ribosomal RNA real-time polymerase chain reaction (qPCR) as the reference test. Among 5,966 persons screened using mRDTs, microscopy, and qPCR tests from 2018 to 2021, 14% (832) were mRDT-positive. Twelve percent of these (98/832) were negative by both microscopy and qPCR, with children overrepresented among those with false-positive mRDTs. Among those who were mRDT-negative, 22% (1,136/5,134) tested qPCR-positive, predominantly because of low-density parasitemia (92% had <100 p/µL by qPCR). Among mRDT-negative samples with >100 p/µL, we looked for evidence of hrp2 or histidine-rich protein 3 (hrp3) deletion using two methods, multiplexed qPCR and multiplex bead-based immunoassay. When sufficient parasite material existed for a reliable deletion assessment, 12/34 (35%) had evidence of hrp2/3 deletion by qPCR (nine hrp2-/3+ and three hrp2-/3-), and 20/52 (38%) had evidence of deletion by immunoassay. Only three isolates showed evidence of hrp2 deletion by both assays. In an area of low to moderate transmission in Tanzania, false-positive mRDTs are relatively common (12% of positive tests), and false-negative mRDTs are even more common (22% of negative tests), but hrp2/3 deletion causing false-negative mRDTs remains rare (<1% of negative tests).