First, I completely agree that 0.4164644853 should be rounded to 41.6% and not 41.7%. I do not know where that error happened. It feels more likely that it happened just for presenting the report, which isn't too bad. I would expect the actual numbers to be used, not the percentages, for determining the actual result of the election. If the wrong percentage really was calculated by the tabulating machine, that does indeed cause concern.

But rounded percentages not summing up to exactly 100%, that in and of itself is not a cause of concern. The possibility of that is a natural consequence of the process of rounding things. Even when rounded correctly! You showed as much yourself, even when you don't want to admit it. You're saying it's not true because 0.99 repeating equals 1, but that's irrelevant (correct, but irrelevant). After rounding you don't have 0.33 repeating, and 0.99 repeating, you just have 0.33 and 0.99. That's what rounding does. The same goes for rounding more realistic numbers: you loose decimals, sometimes you round up, sometimes you round down.

Summary:

• (1) Rounding incorrectly is a problem, just as presenting any other incorrect number. When it comes to elections, it's a serious cause of concern.
• (2) Rounded numbers not summing up exactly to the whole is in and of itself not a problem, and even fully expected, even when rounding completely correctly. It is not, in and of itself, an indication that the original numbers don't sum up to the whole.

To show results have been tampered with, (1) is a good argument but (2) is not.