The source forum has a link in the list of threads, which you probably know already. Do you mean in the destination forum? Interesting question.
Have you seen situations where it was confusing what the source forum of a thread was? Like you say, usually if we move a post to a different forum and it might be confusing (especially for homework threads), we try to add a note in the OP to mention that the thread has been moved.
If we move a thread from, say, Quantum Physics to Classical Physics, we would not usually mention anything in the thread (but the OP is notified by default about the thread move).
Sorry @berkeman, yes, in the destination forum. I've been caught out twice, so it's not a biggie, and you've just suggested use cases where it probably doesn't make sense for anyone to be alerted. Hmmm, might not be that useful to warrant coding anything up
BTW, the whole UI of PF is terrific. Compared to many other sites, the clearly numbered posts - easy for referencing and also for knowing the sequence of comments - lack of "up vote" (who thought that was a good idea? Just lets trolls and malcontents bubble crap to the top), lack of evident text limit in a comment so you don't have to worry about cramming your thoughts into a word cound, and content formatting controls make for engaging discussion. Plus the thoughtful moderation! That's rare and it's gold
It is a bit startling to see a "Somebody started a thread called Something" alert, look at the thread and see a couple of responses, and then a while later get the same alert for what turns out to be the same thread because it's been moved from one forum that I watch to another. In a similar vein, I suspect that once or twice I've seen a thread that mentors have subsequently hidden and then unhidden and had the same glitch-in-the-Matrix effect. A different alert text for "thread was moved/unhidden" would be nice, but it's not a particularly serious thing.