I just shot a watcher class, the first type, and it lost a Imp. Hover unit. However, the popup followed the bot out of the room, down a hallway, and into some other place I haven't quite been in the lower left quadrant of the view. This reveals more about the bot's action than the movement trails do since I can't see that far / through doors / etc.
I'm aware of this one, but decided to wait and see if anyone cared about it enough, including the fact that a fix for it will cause other problems. It's a fairly rare occurrence, generally happening when you shoot at Watchers with a big volley and use up lots of time while they zoom away. But removing those labels will mean essentially destroying labels for any robots that leave your FOV, so you could lose access to a lot more information when fighting in confined spaces, which could be rather annoying.
Maybe we can try it and see if a more nuanced solution is required, but it would be too inefficient to do a lot of extra accurate checking on label validity every turn.
I also note that there's nowhere to see what lost what part you shot off if you blink and miss it on the map.
It appears in the message log, but yeah it doesn't show who the part belonged to. That could be added, though it was originally left out to keep log clutter down, since you generally do know who was shot and lost what.