Insults are – well – supposed to be insulting. OMG, I just insulted someone and they're like so offended!
I'm sure 'mouthbreather' is purely a reference to the slack-jawed gormless look that people who, for instance, appear in crime photos have. James Smith, 47, of Cudchew North appeared in court charged with exposing himself in Sports Direct. And there he is, jaw hanging wide like a broken lantern, staring at the camera. Say cheese, James, say cheese. Don't worry, we're not asking you to spell it. And put that away. Sigh.
I know it's a thoroughly modern pastime to define words in such ways as you can then find them offensive (bonus points if you can tweet about it) but I also think that words like idiot, moron, and cretin have moved far beyond specific medical references.
Retard is pretty high on the generally offensive list mind (though pretty generic in the US, like spastic, where it doesn't really resound with the sense it has in British English, though I still cringe), and I don't think anyone who wasn't an idiot would use words like spastic and mong. Of course, I grew up during the era when every school playground was filled with the chant of 'Joey! Joey! Joey!' Don't ever let it be said that 99% of children are little more that miniature sociopaths (and if you think yours are better, they're probably not, you're just hormonally programmed not to realise).
Mind you, I'm a non-nasal breather, with a speech defect, and a lazy eye (I made the rest of me lazy so as to avoid making it stand out).