The trailing backslash must be the last character on the line for it to be interpreted as a continuation command. No comments or even whitespace are allowed after it.
You should be able to put comment lines in between your commands
# output MYSQLDUMP file
cat ${MYSQLDUMP} | \
# simplify the line
sed '/created_at/d' | \
# create some newlines
tr ",;" "\n" | \
# use some sed magic
sed -e 's/[asbi]:[0-9]*[:]*//g' -e '/^[{}]/d' -e 's/""//g' -e '/^"{/d' | \
# more magic
sed -n -e '/^"/p' -e '/^print_value$/,/^option_id$/p' | \
# even more magic
sed -e '/^option_id/d' -e '/^print_value/d' -e 's/^"\(.*\)"$/\1/' | \
tr "\n" "," | \
# I hate phone numbers in my output
sed -e 's/,\([0-9]*-[0-9]*-[0-9]*\)/\n\1/g' -e 's/,$//' | \
# one more sed call and then send it to the CSV file
sed -e 's/^/"/g' -e 's/$/"/g' -e 's/,/","/g' >> ${CSV}