In the first part of this verse, Oliver Cowdery initially wrote the instead of a before war. Since this war is mentioned here for the first time, the use of the definite article seems strange. Oliver crossed out the the and supralinearly wrote a. Since the correction appears to have been virtually immediate (there is no change in the level of ink flow), the critical text will accept here the indefi- nite article a as the original reading.
Later on in this passage, Oliver Cowdery initially wrote the singular their war in 𝓞; then somewhat later he inserted the plural s (the s is somewhat raised off the line). The ink flow for the s is less distinct and somewhat smeared. This smeared s does not show any erasure; we therefore conclude that the change from the singular to the plural was not reversed. Oliver probably initially wrote the singular because earlier in the passage the text read “and thus commenced a war betwixt the Lamanites and the Nephites”. The singular their war seems perfectly reasonable here; thus there would have been no motivation for Oliver to consciously emend their war to their wars. Oliver probably made the correction to their wars after reading the text back to Joseph.
There is strong evidence that the plural their wars is correct since later in the text, when Mormon returns to his promised account of “their war(s)” in this particular year (“the eighteenth year of the reign of the judges”), he once more uses the plural wars:
There is a direct link between Alma 35:13 and Alma 43:3; thus the use of the plural their wars in Alma 35:13 is undoubtedly correct.
Summary: Accept in Alma 35:13 Oliver Cowdery’s two corrections in 𝓞, the change of the war to a war and the change of their war to their wars; the first correction was virtually immediate, while the second probably occurred when Oliver read back the text to Joseph Smith.