I felt the same about Arya being stabbed in GOT. Her injuries looked to be the kind you would be lucky to survive with the benefit of a modern hospital with the best medical staff. Yet she was soon back to normal after a short spell of care from another character who wasn't even a healer.
The film "Stuart Little" annoyed me no end. I know a talking child size mouse is impossible, but I could have accepted it if some explanation was given such an experiment or radiation.
A good example of making a far fetched plot believable is the lovely Dutch children's classic "The Cat that came in from the Roof" which makes a cat turning into a woman believable. A must read if you like cats whatever your age!
I can accept dragons, talking trees, amazing feats by the hero, talking animals and all sorts of fantasy, but some plot details just annoy me no end!
In the LOTR films, the line "Let's hunt some Orc" sets my teeth on edge. It is so unlike Tolkien's language and in British English is ungrammatical. It would sound much less jarring as " Let us go and hunt some Orcs." Casual language doesn't work in historical/ fantastical settings. My pet hate in LOTR and other historical fanfiction is "OK".