Just to add my 0.02c worth:

Make use of indenting in script writing!!! It makes maintenance on your script just SOOO much easier.

Trying to find a nested elif command in amongst all you "echo"'s was quite something:

#!/bin/sh
#
# Set local variables
USER=`/usr/bin/whoami`
ACCOUNT=Compaq
HOSTNAME=`/usr/bin/hostname`
DATE=`/usr/bin/date "+%Y%m%d"`
TEMP=`find . -name "gem*" | wc -l`
TEMPALL=`find . | wc -l`
# Purge old Log Files
#find /users/agaff/nospace/logs/ -name "*.txt" -atime +1|xargs rm -f
# Main Screen
clear
echo "<1> Delete GEM log files on host: " $HOSTNAME
echo "<2> Delete ALL Files in the /var/tmp ( maintenance only ) "
echo "<3> Exit - no files to be deleted"
echo ""
echo " Enter 1 or 2 or 3"
read ANSWER
if [ $ANSWER -eq "1" ]; then
clear
echo "Examining Log Files for host: " $HOSTNAME
echo ""
if [ $TEMP -eq "0" ]; then #(this is where it bombs out)
echo
echo
echo "*******************************************"
echo "There are no log files to be deleted from host:" $HOSTNAME
echo
elif [ $TEMP -gt "0" ];
then
echo "****************************************"
echo "There are " $TEMP "log files that can be deleted from host:"
$HOSTNAME
echo ""
echo ""
echo "<1> Delete GEM log files on Host" $HOSTNAME "in the /var/tmp directory"
echo "<2> Exit - no files to be deleted"
echo ""
echo " Enter 1 or 2"
echo""
read ANS1
if [ $ANS1 -eq "1" ]; then
clear
echo ""
echo ""
echo "Deleting GEM Logfiles Log Files"
#mkdir -p /users/agaff/nospace/logs/
#find /var/tmp/ -name "gem*" -atime +3 > /users/agaff/nospace/logs/$DATE"-"$HOST
NAME"-logs".txt| xargs -f >/dev/null 2>&1
echo ""
echo "*******************************************"
echo "Tmp Logs are now deleted and logfile updated"
echo ""
echo ""
elif [ $ANS1 -eq "2" ]; then
echo "Exiting"
else
echo "Invalid selection, exiting..."
exit
fi
fi
fi



Here endeth our readability lesson for today...