Land plant organellar genomes have extremely low rates of point mutation yet also experience high rates of recombination and genome instability. Characterizing the molecular machinery responsible for these patterns is critical for understanding the evolution of these genomes. While much progress has been made towards understanding recombination activity in land plant organellar genomes, the relationship between recombination pathways and point mutation rates remains uncertain. The organellar targeted mutS homolog MSH1 has previously been shown to suppress point mutations as well as non-allelic recombination between short repeats in Arabidopsis thaliana. We therefore implemented high-fidelity Duplex Sequencing to test if other genes that function in recombination and maintenance of genome stability also affect point mutation rates. We found small to moderate increases in the frequency of single nucleotide variants (SNVs) and indels in mitochondrial and/or plastid genomes of A. thaliana mutant lines lacking radA, recA1, or recA3. In contrast, osb2 and why2 mutants did not exhibit an increase in point mutations compared to wild type (WT) controls. In addition, we analyzed the distribution of SNVs in previously generated Duplex Sequencing data from A. thaliana organellar genomes and found unexpected strand asymmetries and large effects of flanking nucleotides on mutation rates in WT plants and msh1 mutants. Finally, using long-read Oxford Nanopore sequencing, we characterized structural variants in organellar genomes of the mutant lines and show that different short repeat sequences become recombinationally active in different mutant backgrounds. Together, these complementary sequencing approaches shed light on how recombination may impact the extraordinarily low point mutation rates in plant organellar genomes.