Great add on thanks for all the hard work!

per request:
I multi-tag:

1. join LFR
2. tag rare
3. drop from group
4. alt+f4
5. login another of my 6 120 alts
6. rinse/repeat until lfg delists

I'm also new to rarity...
rarity, it seems, only counts the mobs I loot? Other addons like saved instances track counts based on if the daily quest was completed (I can pin a rare elite to track i.e. soundless).
if rarity's expected behavior is to only track counts based on looting, I'm suggesting changing tracking (or allow it to contribute) to completing the daily quest. Its closer to the source of truth, I can get credit on a kill, get a mount thru the mail, without ever looting a corpse.
thanks

PS.
also my screen freezes when i hover over the minimap icon if mounts are expanded, because the list is large. whatever it does on the mouse hover event should probably be moved to some sort of addon loading event so it happens only once (if you can). no need to repeat work to show relatively static data.
thanks again

Rarity supports a number of detection methods, such as looting (NPC), combat log events (BOSS), opening containers (ITEM) and custom ones as well. I don't think it can recognize quest flags changing, though, and I'm not sure how easy it would be to implement this behaviour and make sure it always works/doesn't break anything.

The second problem is a known issue; the tooltip library can't handle many items because it generates too many lines and it's always iterating over all of them when displaying the tooltip IIRC. Not sure how this can be fixed with the current architecture, the code is a huge mess and I don't have time to improve it much. So for now, I'm afraid there isn't a good solution that I'm aware of.