Use the following script:

#! /usr/bin/env bash
#
# Run parallel commands and fail if any of them fails.
#

set -eu

pids=()

for x in 1 2 3; do
  ls /not-a-file &
  pids+=($!)
done

for pid in \\"${pids[@]}\\"; do
  wait \\"$pid\\"
done

OR use the simpler script if no error is expected:

#!/bin/bash

sleep 2 &
sleep 3 &
sleep 1 &

wait

echo Finished.