It would be interesting if they published the revised count by Senator and Parish so that the exact nature of differences could be seen, because of course, while not materially effecting the result, other Senators also had different counts in the end.
If there is enough exactness in the system, then a small percentage of errors will not make a qualitative difference, but understanding how those errors are caused can help make the system more robust in the future.
Apparently, one common error was scanning along a sheet with names at one side, and numbers across, meant that it was easier for the eye to slip from one line to another.
A study by researchers at Rice University showed that hand counting of votes in post-election audit or recount procedures can result in error rates of up to 2 percent.
Michael Byrne, associate professor of psychology at Rice said:
“It is probably impossible to completely eliminate errors in hand counting of ballots. However, there are new auditing methods that capitalize on advanced statistical procedures that can help ensure that final election results better match what is actually on the ballots. It is important that we become aware of the limitations of current methods and develop alternative ways to improve the accuracy of election results.”
For most elections, even a 2 percent error won't change the results, but it can happen.
But the bottom line is that there will always be counting mistakes – but as long as the errors are unsystematic, they will usually cancel each other out. In the aggregate you'll have an estimate quite close to the real result.
So the voting system is not strictly speaking “robust” but “robust enough for practical purposes”.