I don't think checksum is a fair metaphor for anything happening in biological systems.
> Most mtDNA between humans is the same
And most DNA is also the same. A percent difference is the kind of thing that would require millions of years of divergence to develop.
> mtDNA is only 16,569 base pairs long
This is really not so precise. There will be a mixture of lengths due to insertions and deletions, even in the same individual, even in the same cell.
> The differences between mother and child are almost always due to the father's contribution, and not to mutations.
Do you have a citation for this?
[1] Sequence and organization of the human mitochondrial genome (1981). https://www.nature.com/articles/290457a0
Even if you assume that the 100% of the mitochondria comes from the mother, there are well known cases of mother that have a mix of normal and defective mitochondria and the children have a similar mix of normal and defective mitochondria. In this case the variation of the proportion of the normal and defective mitochondria between the mother and the children can cause that some of them get a worse version of a desease.