I think you've at least partially described Dramatic Irony.
Irony that is inherent in speeches or a situation of a drama and is understood by the audience but not grasped by the characters.
The audience is aware of something that a character is oblivious to. This is used for drama as well as humour. If this is not quite specific enough, then already mentioned is the prospect of the idiot plot, which is described as "any plot containing problems that would instantly be resolved if all of the characters were not idiots."
Also, whilst looking at an article on elements of satire, I found the heading Potential Problems with Satire, with this warning -
Misunderstanding: Audience may think the satirist is being serious.
In your question description, you mention South Park and deliberate sarcasm (aka verbal irony, an aspect of satire) being misinterpreted for a humorous effect. Perhaps a makeshift label ought to be 'Extreme Misunderstanding,' or something of the sort, if you truly feel that 'dramatic irony' is too general.
For one last consideration regarding your Harry Potter example, I refer everyone to the adjacent comment, which accurately describes two literary effects dealing with character names.
Dictionary.com