I still wished for the answer to this old question, so I'll share what I finally came up with. This is a hack and not as pretty as I wish, but I add comments by adding a fake search. In the example below, before each complex set of terms, I add "SUMMARY !~ "♥♥ ".
SUMMARY !~ " ♥♥ No subtasks of stories in backlog: ♥♥ " AND issueFunction not in subtasksOf("type = story AND status = backlog") AND SUMMARY !~ " ♥♥ Filter for members of that team: ♥♥ " AND filter = 25233
or
SUMMARY !~ " ♥♥ No subtasks of stories in backlog: // " AND issueFunction not in subtasksOf("type = story AND status = backlog") AND SUMMARY !~ " \\ ♥♥ Filter for members of that team: ♥♥ // " AND filter = 25233 AND SUMMARY !~ " \\ ♥♥"
The !~ prevents the SUMMARY search from messing up your real JQL query. There is a chance that my comment could actually be found inside one of the results, so adding ♥♥ makes it highly unlikely. If your computer can't make that character (press Alt-3 and let go), using ** or other combinations may work for you.
I also like how the ♥♥ and the spaces to make the comment stand out, but perhaps there are better characters like ☻ or ♫ or -- or //. Sadly, [] and () are not allowed. Any spaces must be inside the quotes to be preserved when you save the query.
Sometimes I paste long queries into a programming tool like Notepad++ and make a User Defined Language to clarify the (sections). But note that the special characters don't transfer correctly.
That's the best I can come up with until this feature request is voted up enough and fulfilled:
https://jira.atlassian.com/browse/JRASERVER-20455