Diffuse ionized gas (DIG) is prevalent in star-forming galaxies. Using a sample of 365 nearly face-on star-forming galaxies observed by Mapping Nearby Galaxies at APO, we demonstrate how DIG in star-forming galaxies impacts the measurements of emission-line ratios, hence the interpretation of diagnostic diagrams and gas-phase metallicity measurements. At fixed metallicity, DIG-dominated low ΣHα regions display enhanced [S II]/Hα, [N II]/Hα, [O II]/Hβ and [O I]/Hα. The gradients in these line ratios are determined by metallicity gradients and ΣHα. In line ratio diagnostic diagrams, contamination by DIG moves H II regions towards composite or low-ionization nuclear emission-line region (LI(N)ER)-like regions. A harder ionizing spectrum is needed to explain DIG line ratios. Leaky H II region models can only shift line ratios slightly relative to H II region models, and thus fail to explain the composite/LI(N)ER line ratios displayed by DIG. Our result favours ionization by evolved stars as a major ionization source for DIG with LI(N)ER-like emission. DIG can significantly bias the measurement of gas metallicity and metallicity gradients derived using strong-line methods. Metallicities derived using N2O2 are optimal because they exhibit the smallest bias and error. Using O3N2, R23, N2 = [N II]/Hα and N2S2Hα to derive metallicities introduces bias in the derived metallicity gradients as large as the gradient itself. The strong-line method of Blanc et al. (IZI hereafter) cannot be applied to DIG to get an accurate metallicity because it currently contains only H II region models that fail to describe the DIG.