And `date` returns a timestamp with seconds precision.

`time sh -c 'if [ "$(date)" != "Sat Oct 31 16:00:00 EDT 2015" ]; then sleep 1; fi'` took around 1.010 seconds on my machine, but that includes starting a new shell, so there's probably a much smaller than 1% chance that that particular second will be missed.

EDIT: here's a little program to test this:

    #!/usr/bin/env bash
    while true; do
      target=$(expr $(date +%s) + 2)
      while true; do
        now=$(date +%s)
        if [ "$now" != "$target" ]; then
          if [ "$now" -gt "$target" ]; then
            echo "FAIL :("
            break
          else
            sleep 1
          fi
        else
          echo "OK! :)"
          break
        fi
        sleep 0.1
      done
    done

Adjust the "sleep 0.1" to increase or decrease the perecentage of failures. Remove to see that it (almost) never fails.

Yes, but presumably it rounds that last number, right? So as long as it ticks somewhere between 15:59:59.50 and 16:00:00.49 it should run?