Opabinia regalis was four to seven centimetres long, had five eyes on stalks all pointed upward, a mouth that faced backward, and a single flexible hose on the front of its head ending in a grabbing claw. It lived in the Cambrian, it is not closely related to anything alive, and when a paleontologist first showed the reconstruction to a room of his colleagues, they laughed at him.
That last part is the reason this belongs in a newsletter rather than a textbook, so it is worth being careful about it. See the note below.
The best writing on this animal anywhere. Dresow's actual question is why bizarre Cambrian fossils stopped being called "problematica," and the answer is that phylogenetic systematics and the stem group concept gave the field somewhere to file them. The fossils did not get less weird. The filing system got better.
The line to use: "Five eyes perched upon little stalks. All of them, it seems, pointed upwards. The whole setup is faintly ridiculous." And the one with weight: "Opabinia did not have to conform to the demands of arthropod, or any other, design."
Recent, readable, and the source that carries the laughter anecdote in a citable form. Also the cleanest plain-language anatomy walkthrough: the lateral swimming flaps, the backward-facing mouth, the proboscis as a feeding arm that passed food back under the head. Notes that only a handful of specimens are known.
The Royal Society's own retrospective on the paper that started it all, published for the 350th anniversary of the journal. This is the scholarly account of why Whittington's reconstruction mattered: it was the first serious demonstration that the Cambrian contained body plans that fit nowhere in the modern tree.
Illustrated reconstruction with the anatomy labelled, from a project devoted to depicting Cambrian animals as living organisms rather than fossil diagrams. Useful if you want a picture that shows how the proboscis actually worked.
You asked what it would mean to have this thing as a sports mascot. The commercial answer is that you would not be first. Opabinia has a small but real plush toy industry.
A reviewed, photographed plush of the animal, and the source of the nickname "bini." Proof that somebody already solved the design problem, and evidence for the claim that this animal has a small devoted fandom.
A second, unrelated commercial plush. Two independent manufacturers is the difference between a curiosity and a small market.
The design problem is genuinely interesting and mostly unsolved. Five eyes reads as either menacing or comic with almost no middle ground, and the proboscis is a gift for a costume (an actual working grabber arm on the front of the head) and a nightmare for a logo, because at small sizes it turns into a smudge. Every existing plush solves this the same way, which is to make the eyes large and friendly and let the nose do the work.
The honest naming problem: there is no good short form. The Fighting Opabinia does not scan. The internet has settled on calling them "bini," which is what one of the plush lines is named, and which is roughly a thousand times more marketable than anything derived from the full binomial.
Solid on taxonomy, specimen counts, and the history of interpretation. Has none of the comedy and hedges the laughter story into invisibility.
Opabinia is the best available argument that evolution ran experiments it later abandoned. Five eyes was tried. Five eyes did not take. Nothing alive today has anything like it, and the fossil sat in a drawer for fifty years before anyone worked out what they were looking at.
The reason you do not hear about "problematic fossils" anymore is not that they got less strange. It is that the stem group concept gave paleontologists somewhere to put them.
Sources
All resources listed above with direct links. Foundational paper: Whittington HB. "The enigmatic animal Opabinia regalis, Middle Cambrian, Burgess Shale, British Columbia." Philosophical Transactions of the Royal Society B 271 (1975): 1–43.