Whether somatic mutations contribute functional diversity to brain cells is a long-standing question. Single-neuron genomics enables direct measurement of somatic mutation rates in human brain and promises to answer this question. A recent study (Upton et al., 2015) reported high rates of somatic LINE-1 element (L1) retrotransposition in the hippocampus and cerebral cortex that would have major implications for normal brain function, and further claimed these mutation events preferentially impact genes important for neuronal function. We identify errors in single-cell sequencing approach, bioinformatic analysis, and validation methods that led to thousands of false-positive artifacts being mistakenly interpreted as somatic mutation events. Our reanalysis of the data supports a corrected mutation frequency (0.2 per cell) more than fifty-fold lower than reported, inconsistent with the authors' conclusion of 'ubiquitous' L1 mosaicism, but consistent with L1 elements mobilizing occasionally. Through consideration of the challenges and pitfalls identified, we provide a foundation and framework for designing single-cell genomics studies.