How 'close' can ♦ moderator elections on Stack Exchange get? Has there been an election where a single vote would have made the difference? The Spring 2018 election on Stack Overflow was quite close, percentage-wise; the final difference between the remaining candidates was 17 votes (only 0.05% of the number of ballots). One of the most recent pro-tempore elections, on Drones Stack Exchange looks to have been decided by 1.6 vote (a fractional number; this is a property of the STV system).
It appears that today's results from the Code Review election resulted in 224.05 "votes" for Mast and 224.32 "votes" for Peilonrayz, so a difference of 0.27 out of 767 total ballots:
This is even closer than the other answer by Rand al'Thor since the difference in voting percentage was less than 0.1%, versus 0.2% in that case!
However, that election on Biblical Hermeneutics was closer in a different sense, since there were 3 candidates almost neck-and-neck with each other in the final rounds, for the last 2 positions, whereas in Code Review there were only 2 candidates neck-and-neck with each other in the last round, competing for one position.
In the absence of any mention of any other election even remotely as close as this, I'm going to propose that the likely answer is the 2020 Biblical Hermeneutics moderator election, which finished today (27 October 2020). It was a three-slot graduation election, with just four candidates. In the final round of vote counting, the difference between the 3rd and 4th candidates was just 0.2 votes, with the losing candidate just 0.15 votes below the threshold. There were a total of 110 users voting, making this difference 0.2% of the overall electorate.
This week we had two very close elections, and unlike the case of the April 2021 Code Review election in which the race was close between 3 users competing for 2 positions (and eventually it was decided that all three of them would become a ♦mod), both of these recent July 2021 elections were close between 4 users competing for 3 positions, and the 4th place candidate was within 2% of the 1st place candidate in both instances!