If my ID here is correct, this pouched anole: https://www.inaturalist.org/observations/131501728. Only 25 observations on iNat. However… this species is so rare I worry I may have misidentified it. Should any anole experts have input, I would love it!
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In terms of rarity worldwide, this young scalloped hammerhead I caught a few years back. Don’t worry, I ensured it got back in the water and swam off safely.
In terms of infrequency of observations, this Spanish flag, a species of wrasse from the Gulf of Mexico and Caribbean Sea that only has two sightings on iNaturalist so far
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If I had been to the Galapagos to look for those tortoises I might win this contest 
I have found birds which are not exactly rare in Hong Kong but which one is unlikely to find oneself. For example, your profile picture reminds me of the flock of Chestnut-flanked White-eyes I happened to come across only a few weeks ago. After that flock left, a friend of mine joined me and learnt what he had just missed.
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Regarding observations of things that are verifiably endangered, Frasier Fir https://www.inaturalist.org/taxa/136317-Abies-fraseri is, I think the only one I have checked off. Mostly because you have to climb a mountain in Appalachia to find any.
As far as least observations go (that isn’t a weird, hard to ID fungus) - maybe this little beetle? https://www.inaturalist.org/observations/114674025 its not a research grade obs yet but it seems to match the other recorded pictures - its just an absolutely itty bitty species (MAYBE 2-3mm long, tops) so I’m sure it gets overlooked.
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In terms of observations, most likely the Gansu Leaf Warbler, which now only has 11 observations. Of course it helps that I am currently living in Gansu, and not many birders come here.
https://www.inaturalist.org/observations/142512966
Though as for rare animals it wouls have to be the Crested Ibis, once thought to be extinct, but luckily due to a breeding programme in Yangxian (not too far from where I live), numbers are up.
Crested Ibis (Nipponia nippon) on 03 July, 2019 at 03:53 AM by Roy · iNaturalist
I do have one observation of a species with only 3 other observations: The Chinese Red Pika. However, I can’t count it yet as nobody else has confirmed it yet: Chinese Red Pika (Ochotona erythrotis) from Langmusi, Luqu County, Gannan Tibetan Autonomous Prefecture, Gansu, China, 624504 on 09 August, 2021 at 03:53 AM by Roy · iNaturalist
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My rarest is technically a fungus but is probably a violet coral fungus that I found in Minnesota: https://www.inaturalist.org/observations/129431273
My second rarest is a tar weed that has nearly been taken out from the western half of Washington. The only one I have ever found was on the Olympic Peninsula: https://www.inaturalist.org/observations/57048141
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I think its the Mantis Religiosa or Aedes albopictus (i’m from germany).
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The rarest taxon I’ve ever seen was almost certainly an insect that I did not pay any particular attention to.
Once we get out of large and / or charismatic organisms (vertebrates, orchids, cacti), it’s probably reasonable to assume that if we know how rare a taxon is, it’s not especially rare.
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hm. for me, probably the Kirtland’s warbler, a couple decades ago when the population was even smaller.
I’ve seen a number of species near the edges of their ranges, in places where they are considered locally rare. mostly plants, but a few others, too.
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Ha! I dug back into my photos and sure enough I did photo a silversword. Just added to iNat.
I wonder what else I have lurking in my old photo folders.
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I wondered why a plant of the Sandwich Isles popped up in my updates.
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I don’t think so. Pretty sure they aren’t native, hence I said it was owned by someone or someone’s pet. Was “rare” because it became somewhat a rumor among the neighborhood.
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Alabama Snow wreath wild colony
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The Diptera enthusiasts here might appreciate this:
Back in 2016, in a reserve in the northern Midlands region of South Africa, I came across this Small-headed Fly; it seems mine is the only observation of it anywhere in the world for iNat
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the head is so small you can’t even see it on the picture
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I had a similar encounter in the south american Andes once… it was fun figuring out what it was
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I know right? And notice the mimicry of Honey Bee colours and patterns
I wonder what the backstory is there, ecologically speaking?
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Awesome!
Atleast my observation isn’t the only one of the Small-Headed fly family then 
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Looks like a few observations for Acroceridae on iNat. Noticed there’s an observation from here in South Korea as well, putting the range up to at least three continents. Guess that’s something for me to keep an eye out for now. :)
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