I've been thinking about how handy it could be if you were notified immediately that you could no longer complete an achievement you were working on.
Say you are trying Split Personality: as soon as you kill one of the images, a hidden 5 second timer should start and if you kill the next one after that you should be told immediately. That way you can wipe it and try again.
Ideally, such an addon will automatically detect which achievement is being attempted. This could be simple enough for boss fights and quest-related achievements. The addon shouldn't need to do anything for achievements that are already catered to by the Blizzard achievement tracker, although automatically switching the tracker to the right achievement could be something within it's purview.
There is a finite number of achievements in the game, and there's probably only a dozen or so cases where I think this could be really useful. Off the top of my head: Shocking, King's Bane, Shatter Resistant, etc.
There are some like Oh Novos! that just can't be tracked. But I think that one in particular is fairly easy to monitor.