As the Charms lesson and common sense equally stress, a proper pronounciation is essential for your spell to actually work. Not taking into account silent spellcasting, there is a language element in almost every possible application of magic. But there are many possible problems that may hinder a young witch or wizard to be able to intonate these incantations properly.

There are many different speech disorders. The numbers of occurrence of these disorders are surprisingly high: It is estimated that in the United States, one out of ten people suffers from a communication disorder. Almost a quarter of all school children receive services for speech or language disorders (1). As these numbers can be likely applied to Hogwarts as well, one can easily assume that some of those eligible to attend Hogwarts suffer from a language or speech disorder. These disorders can occur in different ways: most commonly known are either mutism or stuttering. Both certainly have an influence on a potential student's ability to successfully cast a spell.

As a first case study, one can take a look at Quirinius Quirrell, who taught Defence against the Dark Arts in Harry Potter's first year of school and was known to be stuttering. Following the course of the books featuring Harry Potter's life, there is not even once a situation in which Quirrell is casting a spell non-silently. As his stutter is faked, it is unclear whether his ability to cast a spell silently is due to him not stuttering usually or whether this is a common occurrence in stuttering people. Nevertheless, it is easily seen that most, if not all, incantations are of a form that would be changed by a stuttering pronounciation, making the spell's effect possibly dangerous.

Another case to be discussed is the education of mute people. Looking at an education in the non-magical world, some mute people learn to speak anyways, though their pronounciation is sometimes a little off. Hence, it should certainly be possible for a mute person to learn to speak an incantation, but these slight differences are potentially problematic. If a person is not able to speak at all, they would however still be able to learn to write and thus think in the same words that we do. Hence, the possibility of them using the same spells as we do, though silently, should exist. But it appears rather hard to learn to cast but silently, and I am unsure whether this is possible at all. An alternative would be casting in sign language, but as this language often requires the use of both hands, I cannot imagine how it would be possible to cast that way.

Summing this up, there are several aspects to still be researched:

1. How does spell casting interact with stuttering?
2. If there is some kind of interaction, is it possible for a stuttering person to learn non-silent magic?
3. Is there any way to teach magic to a mute person?
4. What happens to those witches and wizards who are unable to even form words due to aphasia? How are they protected from their magic lashing out?

Is there even any literature about that topic here at Hogwarts? I'll have to go looking for it!

Sources:

• (1) https://en.wikipedia.org/wiki/Speech_and_language_impairment