I went into a chat room, and someone said something offensive to me. So I flagged it as offensive. Almost immediately, the chat message was edited into something nicer. When the 10k-ers came into the chat room, the message was already edited into something nicer, so they could not see the offensive message. What should I do in this case?
For starters, the full history of a (non-deleted) message can be seen by all users. Additionally, room owners and moderators can see the history of any messages, deleted or not. Therefore, you're always able to point to the message to provide proof to a moderator for the fact that something offensive was said.
This is an appropriate time to flag a message for moderator support. If you click the drop-down arrow on the lefthand side of a message, you'll see this pop-up:
See at the bottom is the option to "flag for moderator". Unlike flagging as spam/offensive, this option allows you to briefly describe the problem to a moderator, so they can handle it. Additionally, these flags are only shown to diamond moderators, rather than to any user with 10k reputation in chat.
Here, flag the edited message for moderator, explain briefly what happened (e.g. link to this meta question) and they'll take the appropriate actions (such as deleting the message, or purging the revision history etc.)