The detection of mitochondrial DNA (mtDNA) mutations in single cells holds considerable potential to define clonal relationships coupled with information on cell state in humans. Previous methods focused on higher heteroplasmy mutations that are limited in number and can be influenced by functional selection, introducing biases for lineage tracing. Although more challenging to detect, intermediate to low heteroplasmy mtDNA mutations are valuable due to their high diversity, abundance, and lower propensity to selection. To enhance mtDNA mutation detection and facilitate fine-scale lineage tracing, we developed the single-cell Regulatory multi-omics with Deep Mitochondrial mutation profiling (ReDeeM) approach, an integrated experimental and computational framework. Recently, some concerns have been raised about the analytical workflow in the ReDeeM framework. Specifically, it was noted that the mutations detected in a single molecule per cell are enriched on edges of mtDNA molecules, suggesting they resemble artifacts reported in other sequencing approaches. It was then proposed that all mutations found in one molecule per cell should be removed. We detail our error correction method, demonstrating that the observed edge mutations are distinct from previously reported sequencing artifacts. We further show that the proposed removal leads to massive elimination of bona fide and informative mutations. Indeed, mutations accumulating on edges impact a minority of all mutation calls (for example, in hematopoietic stem cells, the excess mutations on the edge account for only 4.3%-7.6% of the total). Recognizing the value of addressing edge mutations even after applying consensus correction, we provide an additional filtering option in the ReDeeM-R package. This approach effectively eliminates the position biases, leads to a mutational signature indistinguishable from bona fide mitochondrial mutations, and removes excess low molecule high connectedness mutations. Importantly, this option preserves the large majority of unique mutations identified by ReDeeM, maintaining the ability of ReDeeM to provide a more than 10-fold increase in variant detection compared to previous methods. Additionally, the cells remain well-connected. While there is room for further refinement in mutation calling strategies, the significant advances and biological insights provided by the ReDeeM framework are unique and remain intact. We hope that this detailed discussion and analysis enables the community to employ this approach and contribute to its further development.