Commenting in a Bash script inside a multiline command

As DigitalRoss pointed out, the trailing backslash is not necessary when the line woud end in |. And you can put comments on a line following a |:

 cat ${MYSQLDUMP} |         # Output MYSQLDUMP file
 sed '1d' |                 # skip the top line
 tr ",;" "\n" | 
 sed -e 's/[asbi]:[0-9]*[:]*//g' -e '/^[{}]/d' -e 's/""//g' -e '/^"{/d' |
 sed -n -e '/^"/p' -e '/^print_value$/,/^option_id$/p' |
 sed -e '/^option_id/d' -e '/^print_value/d' -e 's/^"\(.*\)"$/\1/' |
 tr "\n" "," |
 sed -e 's/,\([0-9]*-[0-9]*-[0-9]*\)/\n\1/g' -e 's/,$//' |   # hate phone numbers
 sed -e 's/^/"/g' -e 's/$/"/g' -e 's/,/","/g' >> ${CSV}

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}

This will have some overhead, but technically it does answer your question:

echo abc `#Put your comment here` \
     def `#Another chance for a comment` \
     xyz, etc.

And for pipelines specifically, there is a clean solution with no overhead:

echo abc |        # Normal comment OK here
     tr a-z A-Z | # Another normal comment OK here
     sort |       # The pipelines are automatically continued
     uniq         # Final comment

See Stack Overflow question How to Put Line Comment for a Multi-line Command.