Undercooked is a rare word that’s used by almost everyone.
As is “half-baked”.
Order placed. Thanks.
And bloody.
I use persnickety alot.
Always gets an eyebrow.
Not all that rare. But people don’t expect it to come outta my mouth. I guess.
would you happen to know of events for rare adjectives? Preferrable on the east-coast
/s
“Television: A new medium—rare, if well done!”
Fred Waring. May 1949.
Well, uh, yes. I mean, infrequent use is pretty much what defines a rare word, so it’s kinda tautological. I mean, what are you trying to ask here? What other possibilities are there? They get exiled to Elba or something?
Here you go, the International House of Logghorea. Over 17K to choose from.
Some words are only rare under ordinary circumstances. Within their specialized field, they’re well used. Anemochory, for instance, would be common in botany. Supernatant is used in several fields, including wastewater treatment.
Hey. I have my own rare words.
Googly. Thingamajig. Wompyjawed. Crampidy.
I gots more. But I’ll stop.
That’s an unusual pick
Ouch.
I hate to disappoint you, but I use the word pleonasm regularly, and most likely so do some of the Indonesian students I taught rhetorical devices to a few years ago. (Also, isn’t there a Doper named @Pleonast?)
Pleonasm is a worthy concept. I favor well-considered pleonasm, but constantly ask myself, “is this repetitive language enhancing what I’m trying to say, either through emphasis or meter, or is it just flabby?”
Twas brillig, and the slithy tove
Did gyre and gimble in the wabe:
All mimsy were the borogoves
And the mome raths outgabe
Google’s webcrawlers are everywhere. 7 hours after your post and it gets the unique hit.
No shit.
“Alot” should win the award for rarest word, since it’s so rare that it doesn’t exist at all! Although an alot is sometimes imagined to be a large furry horned creature, possibly extinct: 
I’m still looking for a place to mention a fulcrum. Or even two, if possible, to make them fulcra.
Even better if they’re non-coaxial. (wink).
Who?
I picked my name as a back-formation from “pleonastic”, another rarely used word. (I know exactly where I discovered it: the Dune Encyclopedia’s entry on Galach talked about “pleonastic pronouns”. I informally studied a lot of linguistics when I was young.)
It’s a similar process as what happened with “all one”, “to day”, “an other”, “in stead”, etc. Enjoy the birthing of a new word!