For messages in chat, clicking on the drop-down icon will allow rude or abusive messages to be flagged. I've noticed that messages in a transcript can no longer be flagged. I seem to recall that it used to be possible. How can one flag a problematic message that is in a transcript for abuse or mod attention?
You can't, at least not from the transcript.
A workaround is to join the room, and keep loading older messages until you get to the message you want to flag. Only moderator flags will work, see here:
a moratorium on messages over, say, 10 days old; if it wasn't flagged as part of the live active discussion, then flagging it after the fact is probably so rare that disallowing that (leaving only mod-flags, which are more obvious when abused) seems reasonable [done - 15 days currently, but open to review]
If the room has a lot of messages, the message is really old and/or you don't want to join the room, there's an alternative: flag a post on the site the chatroom is associated with and clearly state there's nothing wrong with the post itself, but a ♦ moderator should have a look at the chat message you actually would like to flag. It's probably a good idea to state why you're using a custom flag.