Wrong concern
One of the ZeroHedge types is
worrying about accidental problems in stock-trading caused by the end-of-June leap second.
If we're going to worry about this at all, we should be more worried about intentional scams.
Long before atomic clocks, scammers
found ways to use mismatched clocks to run horse-betting rackets. Gather some marks in a room. Feed them a fake broadcast of race results. Either delay the actual radio for a few minutes by audiotape, or pick up the results by ticker and read it in broadcasting style. Because of the delay, you know the results before the bets are placed. There are several ways to skin the marks after they're convinced, but the central point is that you can shape "reality" as seen by the marks.
This trick wouldn't be possible now. You'd have to gather up everyone's Devices, or possibly wi-fi-hack them all to change the time. Neither would work properly.
But in the world of HFT, one second is plenty long enough to reshape reality, provided you know which systems are going to miss the second.