Spatially resolved temperatures in a variety of low pressure flames of hydrogen and hydrocarbons burning with oxygen and nitrous oxide are determined from OH, NH, CH, and CN laser-induced fluorescence rotational excitation spectra. Systematic errors arising from spectral bias, time delay, and temporal sampling gate of the fluorescence detector are considered. In addition, we evaluate the errors arising from the influences of the optical depth and the rotational level dependence of the fluorescence quantum yield for each radical. These systematic errors cannot be determined through goodness-of-fit criteria and they are much larger than the statistical precision of the measurement. The severity of these problems is different for each radical; careful attention to the experimental design details for each species is necessary to obtain accurate LIF temperature measurements.