Answer transcribed from the Brightway Answers interview with speech-language pathologist Amber Kloess:

There is a wide variety.  There is aphasia, or the inability to understand or express language.  This can be verbally through reading or writing, we can see difficulty following directions, and also expressing thoughts and ideas.  Many patients that have had a brain injury have difficulty understanding figurative language and they're very literal in their thinking. Problems with word-finding are also very common.  Along those same lines agraphia or dysgraphia can occur - this is the impairment of written language and can range from mild to severe.  Finally, alexia which is the impairment of reading out loud or understanding written language.

On the speech side, there's apraxia, which is the inability to or difficulty with coordinating muscle movements for producing speech.  This can manifest through distorting sounds, slowing your rate of speech, or exaggerated movements, which we call groping.  Another one is dysarthria, which is weakness in the muscles, which makes speech difficult to produce and understand. There are a variety of types, but usually we see a slurred speech, their intonation may be off, their rate / rhythm of speaking, and then some breathing difficulties as well. There's also neurogenic stuttering, which is stuttering that is caused from some sort of neurological disorder like a brain injury or stroke.  Finally I see social communication challenges on the language side - you may have difficulty following rules of conversation, like talking too much, interrupting others, bringing up inappropriate topics, or trouble initiating conversation.