A thread I've been following has moved at least once, and I think it got moved again (based on another user's comment). I understand moving topics, and think that generally it is appropriately done. If I have already commented on a topic, I get notifications about it. Notifications link to the topic directly, so there's no way to know if it has been moved. A small indicator of where the topic is currently posted could be placed near the poster's name.

Also, topics that get moved into a room after discussion has already started can be confusing for the people in the new room who don't understand the older discussion (such as, "this doesn't go here"). If there's a room label, the next step could be an indicator of movement. "CC, moved from TTC" for example. An admin comment could also notify people things had been moved.