Digital multimeter safety tips include inspecting test leads for damage and ensuring any capacitors are discharged before taking resistance measurements. When measuring resistance, the meter generates a small current to determine the component's resistance. External voltages can damage the meter or provide inaccurate readings. It is important to disconnect power sources and discharge capacitors before taking resistance measurements to avoid electric shocks or damaging the meter. Digital multimeters should also only be used in resistance mode when checking components to prevent damage.