What are Bakhtin's main concerns regarding language?
Bakhtin believed that the basic units of language, such as words or utterances, do not have abstract meanings but are instead affected by the speaker's relationships with other people and the culture of the time. Therefore, Bakhtin concerns himself with the cultural and historical context of language as well as what Bakhtin calls "addressivity" (to whom language is addressed) and "answerability" (the response that language invites). Therefore, language never exists in a vacuum but is affected by its historical context and the dialogue in which it is involved. Bakhtin writes in Problems of Dostoevsky's Poetics, "I live in a world of others' words." In other words, language is not neutral but is affected by other people's meanings. He writes in Speech Genres and Other Late Essays:
"When we select words in the process of constructing an utterance, we by no means always take them from the system of language in their neutral, dictionary form. We usually take them from other utterances, and mainly from utterances that are kindred to ours in genre, that is, in theme, composition, or style. "
As utterances exist in a world of other people's words, utterances in any genre are marked by "heteroglossia," or multiple voices and styles within one work, and the work is "polyphonic," or characterized by many voices. Therefore, Bakhtin is concerned with the way in which language calls upon other people's meanings and operates within a deep cultural and historical context.
Bakhtin was concerned with two main aspects of language: linguistics and literary theory. As my answer to your other question suggests, the two were intimately related in his mind. Basically, Bakhtin was interested in the "dialogical" aspect of language. This means that he thought language involved reaching mutually agreed-upon meanings, not necessarily referencing meanings that already existed. Meanings are always changing according to a number of different factors. But communication depends on being able to reach mutually agreed upon meanings, so language, while always relational, was never completely relativistic. People have an interest in being understood, and in understanding, so they reach agreements as to meaning.