The DNA polymerase (gamma, I believe) that replicates mitochondrial DNA is no better than it needs to be, and it is the high rate of mutation that makes mitochondria useful for following evolution over short recent timescales. Most of the mutations were somatic, and it doesn't matter what variants you have in your liver, they won't be passed to offspring. Mammalian female germline cells don't divide may times, and are mostly dormant, so there are fewer mitochondrial DNA replications to introduce mutations, and they need fewer mitochondria than energy intensive tissues. Hence female germ lines probably have a relatively low mutation rate compared to liver or mucosa or neurons.\nMany of the mutations were in coding sequences and are not seen as the sole type, so presumably are too deleterious to support an individual up to reproductive age, although they may not be significant at a frequency of a few percent in a few tissues.\nWhere heteroplasmy exists from the oocyte it can be transmitted through generations. One documented case is Holstein cows. More notable, Tsar Nicholas II, murdered/executed by Bolsheviks in 17th. July 1918, and his brother who died from disease, shared a heteroplasmy, now lost from their female relatives.\nEvolutionary studies make use of a small number of mutations that are fit for the purpose, meaning stable enough to be reliable and locally common or diagnostic. They have originated among, and spread with, particular human groups. \nLooking at the paper, the mother's mitochondrial type was reproduced in the offspring and was the most frequent type even in tissues with a high proportion of a new mutant type, so it would be identified. Because forensic and phylogenetic tests look for specific established mutations they would find them in any of these cells, so false negatives would be rare. False positives from new mutation are rare, but a known possibility, and examination of other diagnostic sequences would still allow maternity testing. There is a possibility that a small individual sample from historic material would give a deceptive result but again there would be other markers to check and anyway, outside the context of a family tree it would not matter. The transport of female slaves around Europe, Africa, Asia for millenia have ensured that any mitochondrial type could appear almost anywhere.