My check of 65 wicks on 50 pages found that:

• 7 examples (10.8%) fit the original definition.
• 12 (18.5%) were about fantasy creatures inspired by pterosaurs, with varying amounts of realistic-ness.
• 16 (24.6%) were about generally inaccurate pterosaurus, even if they don't fit the "kidnapping eagle-bat-dragon" stereotype.
• 1 (1.5%) was an aversion.
• 11 (16.9%) were either "pterosaurs exist", or potholed under mentions of pterosaurs with no indication of if they fit the trope.
• The remaining 17 (26.1%) were mostly zero-context examples and pantheon pages.

My suggestions for how to fix it:

• Rename the trope into something clearer, like Kidnapping Pterosaur, and move the "general inaccuracies" examples to Artistic License – Paleontology.
• Turn Ptero Soarer into a disambig that includes Artistic License – Paleontology, Giant Flyer, Kidnapping Bird of Prey, Prehistoric Monster, and some other tropes.
• Both of the above.

1. NightmareFuel.Jurassic World The scene wherein the park's pterosaurs have escaped and descend upon terrified tourists in Main Street. And when we say "the park's pterosaurs," we mean ALL of the park's pterosaurs.
2. Meaningful Background Event Just before Ann is attacked by the Pteranodon, you can see it flying by in the distance, because of this it can be easily mistaken for a normal sized bird.
3. Recap.Futurama S 6 E 9 A Clockwork Origin The robot Pteranodon that carries off Fry to feed to its young.
4. Recap.Amphibia S 1 E 08 Taking Charge In Suspicion Island, the teens are attacked by a flock of Pteranodon (called "pterodactyls" as usual) that are, apparently, the clones of Chad's dead brother.
5. ComicBook.Age Of Reptiles (2) While you could argue that they were simply being territorial, the flock of Dsungaripterus that attacked that unfortunate ornithocheirid were being somewhat unrealistically violent toward it.
6. Small Taxonomy Pools (1) Pterosaurs (order Pterosauria) will usually be either Pteranodon, Rhamphorhynchus, or a completely fictional blend of the two; or more occasionally, an eagle-like Quetzalcoatlus, a Pterodactylus or a Dimorphodon. Other species are exceedingly rare.They are often erroneously called "flying dinosaurs".^note Putting this here because the potholed phrase evokes the Kidnapping Bird of Prey part of the description.
7. Recap.Adventure Time S 5 E 40 Play Date The Pteranodon from the beginning uses its wing claws to carry Finn and Jake.

1. Characters.Age Of Wonders Planetfall The Shrike and the Harrier share characteristics with Pterosaurs.
2. DarthWiki.Diamond Phase: Somewhat resembles a pteranodon.
3. Recap.Dinotrux S 01 E 02 Scrapadactyls The Scrapadactyls, metallic scavengers that collect scrap metal to build their nests with.
4. Characters.Pathfinder Dragons Dinosaurs Are Dragons: Sort of. They're pterosaur-like dragons.
5. Series.Captain Power And The Soldiers Of The Future The pterosaur-like Soaron to Lord Dread. At least until Blastarr is created mid-way through the series. Blastarr and Soaron then become Co-Dragons (and bitter rivals).
6. Call a Pegasus a "Hippogriff" The tabletop version depicts The Phoenix as a fire-breathing legless dragon-like creature with membraneous wings, scaly skin and no discernable avian features aside from it's beak. This is an especially odd case, considering the original video game had a much more traditional (albeit somewhat pterosaur-like) phoenix.
7. Franchise.Godzilla Rodan is similarly based on how pterosaurs were portrayed at the time, as a giant beaked reptilian flyer with leathery wings and, in many appearances, a crest that resembles the one of the pterosaur Pteranodon. In fact, his original Japanese name "Radon" is derived from Pteranodon.^note Under Prehistoric Animal Analogue
8. TabletopGame.Shadowrun
   1. Sirens, creatures resembling small Ptero Soarers and possessing hypnotic calls, are believed to have been artificially created as guard animals from unknown reptilian source animals. They weren't suitable for these purposes due to their highly aggressive natures, however, and now live as aggressive predators in wildernesses worldwide.
   2. Our Sirens Are Different: Sirens, creatures of unknown origin and resembling small Ptero Soarers, possess hypnotic calls that evoke profound emotional trances and cause listeners to stand still in a daze or actively walk towards their sources. As sirens are aggressive predators, they are believed to use this ability to hunt.
9. Characters.Silent Hill 1
   1. They resemble a Pteranodon in design, but with longer humanoid legs and human-like torsos between the wings.
   2. Humanoid Abomination: Unlike the Ptero Soarer Air Screamers, these creatures are clearly more human-like in appearance except for the wings and their elongated heads, which are eternally covered in worms.
10. Characters.Gamera They have at least as much in common with stereotypical cartoon pterosaurs as they do with bats.

1. Characters.Carnivores (wicks 1 & 2)
   1. It is always shown flying high in the sky, although the real Dimorphodon is considered to have been a poor flyer. It also lacks the vane at the end of its tail, and it's got pointy wing-tips. On the other hand, it appears to have pycnofibres (hair-like structures pterosaurs possess).
   2. Anatomy-wise it doesn't look that bad, although it's got pointy wing-tips. However, its HD and Reborn version is misproportioned, including a head that's rather small.
2. WesternAnimation.Dino Ranch Pteddy and his mother Maggie are Pteranodons that lack the pycnofibres (fur-like covering) of real pterosaurs and walk on two legs instead of four like they would in real life. However, they're friendly and harmless creatures who help the family around the farm and correctly lack teeth.
3. Literature.Portal Of Evil You can run into a Pteranodon: while its appearence will probably make an expert cringe, at least you fight the beast on the ground, where it's not hindered at all.
4. GravityFalls.Tropes P To Z (1) The "pterodactyl" from "Land Before Swine", which looks like an unholy mixture of all stereotypes, down to the scaly skin, being called a "dinosaur", having eagle-like hindlimbs, leathery wings, having a Pteranodon crest alongside rather mismatched teeth, making chicken-like nests and having zero to no body fat. Strangely enough, though, it walks quadrupedally, like a real pterosaur.
5. Characters.Marvel Comics Savage Land Scaly skin instead of hair-like pycnofibers? Check (occasional hairstyle aside). Bat-like wing structure? Check. Bipedalism? Check. Identified as a dinosaur? Check.^note Holy Word Cruft, Batman!
6. The Theme Park Version The Mesozoic Era gets hit with this trope. Many forms of fictional Dinosaur Media will feature the standard ugly, bloodthirsty carnivores (like Tyrannosaurus rex) and docile, good-natured herbivores (like Brontosaurus), horrifying Sea Monsters that make the shark from Jaws look like a guppy (marine reptiles like Plesiosaurus) and airborne terrors that descend upon helpless creatures on the ground (pterosaurs like Pteranodon). The landscape will almost always be depicted as alien and unfamiliar, with even the flora being impossible to recognize, and the whole thing would be completely covered in volcanoes and molten lakes, with everyday life being a constant fight for survival. Of course, nearly all of these are exaggerated and some, like the volcanoes, are almost totally fabricated. The flora of the Mesozoic wasn't all that different from the flora we have now^note and indeed, many of said fauna such as monkey-puzzle trees and ginkoes are still fairly common today and the animals were, for all intents and purposes, still normal animals. A living T. rex would be no more vicious or terrifying than a modern lion or grizzly bear (aside from being 20-30 times more massive, three and a half times as tall, six times as long and capable of eating an average lion or grizzly in one bite), and on the flipside, a plant eating dinosaur would not necessarily be friendly (modern plant eaters certainly aren't). The sea reptiles and pterosaurs would likely be the same way. What is more, there tends to be an overstatement of the largest and most spectacular creatures in any given area. Dinosaurs came in all shapes and sizes and occupied just about every ecological niche you could think of, and a large apex predator like the T-rex could really only exist in an environment already teeming with life.^note Also, what the heck is going on with this page? About half the examples are general and complain about the "not-we" being uncultured swines, while the other half are about specific works portraying specific subjects in a surface-level way; the latter is more in-line with what's allowed on this wiki.
7. ComicBook.Age Of Reptiles (1) All of them are bipedal, lack sufficient pycnofibres and many of them suffer from the typical Misplaced Wildlife, Mix-and-Match Critters and Anachronism Stew, even worse than the dinosaurs in the stories.
8. Characters.My Girlfriend Is AT Rex Like Trica's Raptor Attack status, his inaccuracies are justified by the nature of the series. At least his wings are supported by one finger rather than being batlike.
9. Characters.The Good Dinosaur All mistakes listed there, plus with the extra fact the specific species probably spent most of their lives soaring above the sea. Instead they spend their days following a storm far out inland.
10. The Magic School Bus S 2 E 3 The Busasaurus The Pteranodons who make a cameo are okay for their time, but aside from the aforementioned Anachronism Stew, they shouldn't be flying over the mainland (Pteranodon was a primarily marine animal).
11. Animation.Speckles The Tarbosaurus
    1. Hairless pterosaurs.^note Under Artistic License – Paleontology
    2. Haenamichnus and Nemicolopterus are both hairless. They also have rather leathery wings - pterosaurs had complex wing membranes -, pointy wingtips and most mistakes seen in 70's pterosaurs. To make matters worse, they're depicted as fish eaters, when in reality they were terrestrial predators not unlike secretary birds.
12. Characters.Godzilla Rodan is basically a textbook example on how pterosaurs were portrayed throught the 20th century, resembling more a plucked chicken with bat wings. For comparison, this is an accurate Pteranodon reconstruction◊. Granted, the Showa and Millenium versions of him have more membrane-like wings, whereas his Heisei incarnation has more blatant bat-like wings. His Heisei version also has a longer beak more similar to those of real Pteranodon. He still has teeth, however. In the case of the Monsterverse Rodan, all this inaccuracies can be justified by the fact he no longer is a pterosaur, but rather an ancient lifeform that happens to look like a pterosaur. His appearance in Singular Point is much closer to the real deal, though, even walking quadrupedally and bearing some small hair, but his toothiness still remains.
13. Series.Koreanosaurus
    1. The Haenamichnus has scaly skin and inaccurate wing folding. It's also shown as eating freshwater arthropods.
    2. Science Marches On: See Ptero Soarer and Raptor Attack. Also, scaly Tarbosaurus and Therizinosaurus.

1. Recap.Prehistoric Park Reimagined E 6 Return Of The King Averted with the quetzalcoatlus, as they are furry, quadrupedal, not at all helpless on the ground, and pick things up with their beaks instead of their feet (which, naturally, are accurately portrayed without talons).

1. ZergRush.Film In the sequel, a group of baby pteranodons attack a kid this way.
2. FunnyBackgroundEvent.Live Action Films Citizen Kane has a scene of Kane and his friends enjoying a beach party. Because the scene was shot on a sound stage, the Florida wetlands in the background are represented by rear-projected stock footage of the jungles of Skull Island taken from The Son of Kong. It's a quick scene, so it's easy to miss that those things flying around the treetops are not birds. So yes, technically there are pterodactyles in Citizen Kane.
3. VideoGame.Biomechanical Toy One of the two most common enemies (besides the T. Rexpy stuffed dinosaurs) in the Lost World stage, where Inguz will face hordes and hordes of stuffed toy pterosaurs coming from everywhere.
4. Flying Flightless Bird A downplayed pterosaur variant on this trope would be in the Dinotopia series, which featured Dimorphodons as the pterosaurian equivalent of an Instant Messenger Pigeon, thus implying long-distance flying ability; later studies would uncover that Dimorphodon would likely have been about as good at flying as a chicken—that is to say, not very, due to its body being heavy and its wings being short. It still could fly, but likely only for short distances and in emergencies. This is justified due to science marching on, as all this wasn't known at the time the books were published.
5. VideoGame.Diddy Kong Racing Purple Pteranodon can be seen flying about in the Dino Domain courses.
6. Small Taxonomy Pools (2) Pterosaurs, usually the 20-foot wide, head-crested Pteranodon of Late Cretaceous North America, and less frequently the gull-sized, fin-tailed Rhamphorhynchus of Late Jurassic Europe. Popular culture often lumps all prehistoric flying reptiles together as "pterodactyls", which is a term restricted only for members of the suborder Pterodactyloidea, particularly its namesake, the Late Jurassic European Pterodactylus.
7. Characters.Genshin Impact Abyss Order Animal Mecha: According to designers team, the Ruin Drake's design is inspired from Tyrannosaurus rex and Pterosaurs which based to Eastern Beliefs that Dinosaurs were considered as Dragons.
8. VideoGame.Fly Or Dieio The Pterodactyl is not the worst depiction, as it correctly has a crest and a toothed beak, and can eat a wide variety of food instead of being restricted to land animals and fish.
9. VideoGame.Zoo Tycoon No pterosaurs appear as adoptable animals, but there is an aviary dedicated for them in the first game: the "Pteranodon House". It doesn't even have Pteranodon. ^note  It has Pterodactylus, Rhamphorhynchus(mispelled Ramphorhyncus) and Dimorphodon.
10. Recap.Rupert S 03 E 01 Rupert And Ginger Rupert befriends a family of Pteranodon.
11. Memes.World Of Warcraft Another fucking horse! ^explanation An incredibly disproportionate number of Alliance mounts are horses, including human and worgen racial mounts along with several reputation-based ones, leading some to feel that Blizzard simply uses a horse when they can't think of anything. While the Horde have a disproportionate number of wolf mounts, it's not to the same extreme. For example, both Alliance and Horde had three new reputation mounts available at the start of Battle for Azeroth. The Horde got a pterodactyl, a bloodswarmer, and a hyena, all but the last of which could fly. The Alliance got three horses.

1. Characters.Carnivores (wick 3)^note The example under Tapejara is just the trope's name and nothing else.
2. YMMV.Turok Evolution went down hill so fast after the Ptero Soarer part. ^note This is a sub-bullet under Scrappy Mechanic, so it's a zero-context example for that reaction.
3. Characters.Star Vs The Forces Of Evil Forces Of Evil: A weird inversion: he is a bird but his Solarian warrior form looks like a reasonably accurate Ornithocheirus.
4. Characters.Dinotrux ^note Commented-out trope-name-only example in Scrapadactyl's folder.
5. Pantheon.Child Archetypes: Pterence: Ptero Soarer, Genki Boy
6. GravityFalls.Tropes P To Z (2) Raptor Attack: The raptor from "Land Before Swine". Like the Ptero Soarer from the same episode, it is guilty of possessing all pop-culture stereotypes: oversized, lack of feathers, pronated hands, and reptilian eyes. It also has two-fingered hands, a feature that doesn't correspond to any known deinonychosaur.
7. Characters.Beast Wars Expanded Universe Natch.
8. Pantheon.Mesozoic Beasts
   1. Rodan, God of Pterosaurs
   2. Portfolio: Flying Pterosaurs, Looks like a Wyvern, Flies at Superspeed, Giant Flyer
   3. All: Stock Dinosaurs (And Pterosaurs)
   4. Petrie: Acrophobic Pterosaur, Cowardly Lion, Ptero Soarer, Innocent Bigot, Third-Person Person, We'll Believe Anything, Has a Very Vivid Imagination, Is Amazed by Pretty Much Everything, Possess teeth despite Pteranodon Meaning Toothless Wing, Once Taunted Sharptooth and Nearly Died in the Process
   5. Those being Apatosaurus, Triceratops, Saurolophus, Stegosaurus, Tyrannosaurus rex, Oviraptor, and Pteranodon.
   6. This is, simply put, a dinosaur’s story… Well, three dinosaurs and one pterosaur to be more precise.
   7. Pterence: Ptero Soarer, Genki Boy
9. ArtisticLicensePaleontology.Live Action TV "Dinosaurs on a Spaceship" had Ptero Soarers, juvenile Tyrannosaurus that look like the adults and typical pop culture raptors.^note Not enough context.
10. Characters.Archipelago Exodus He’d take his sweet time with this one, after that. Maybe saw the crest off and then stab the beast through the jugular with its own crest. Were pterodactyls the ones that had those crests coming out the back of their head?
11. Characters.Crash Bandicoot Villains Scientists In It's About Time, he turns into a giant green-skilled hulk again for the second stage of his boss fight. He performs a second transformation into a Ptero Soarer at the end, but before he can resume the fight he's forced to fly off when this transformation turns out not to agree with his digestive processes much.