should cause waitfor to periodically check for the existence of the indicated file and inform you when it does (by displaying a message or by mail if the -m option is also selected).

Question

Add a -f option to waitfor to have it periodically check for the existence of a file (ordinary file or directory) instead of for a user logging on. So typing:
waitfor -f /usr/spool/steve/newmemo &

Answer 1

There are a lot of changes required to fix how the script parses and tests starting values. For example, you can't just test for a username after getopts because if you're checking for a file, you don't need to also validate a username. Biggest change is the addition of the variable waitfile and all the tests and changes it causes:
#
# Wait until a specified user logs on -- version 4
#

# Set up default values

mailopt=FALSE
interval=60
waitfile=""

# process command options

while getopts "f:mt:" option
do
case "$option"
in
f) waitfile=$OPTARG ;;
m) mailopt=TRUE ;;
t) interval=$OPTARG ;;
\?) echo "Usage: waitfor [-f] [-m] [-t n] user"
echo " -f FILE means wait for the FILE to be created"
echo " -m means to be informed by mail"
echo " -t N means check every n secs."
exit 1;;
esac
done

# Make sure a user name was specified

if [ "$OPTIND" -gt "$#" -a -z "$waitfile" ] ; then
echo "Missing user name!" ; exit 2
fi

shiftcount=$(( $OPTIND - 1 ))
shift $shiftcount
user=$1

# Check for user logging on or for the file to appear

if [ -n $waitfile ] ; then
until test -e $waitfile ; do
sleep $interval
done
else
until who | grep "^$user " > /dev/null ; do
sleep $interval
done
fi

# When we reach this point, the user has logged on

device=$( who | grep "^$user " | cut -c10-16)

if [ "$mailopt" = FALSE ] ; then
if [ -n "$waitfile" ] ; then
echo "File $waitfile now exists"
else
echo "$user has logged on to $device"
fi
else
recipient=$(who am i | cut -cl-8)
if [ -n "$waitfile" ] ; then
echo "File $waitfile now exists" | mail $recipient
else
echo "$user has logged on to $device" | mail $recipient
fi
fi

exit 0