Consistency in pronoun use refers to the point of view you are writing from. There are three points of view: first person, second person, and third person. First person is I and We; second person is you; third person is he, she, it, and they. To be consistent you must write in the same person throughout your paragraph unless there is a very good reason to switch person.
Case refers to using the right pronoun for the right job. The three main cases for pronouns are the subjective case, the objective cases, and the possessive case. You must use the appropriate pronoun for the function the pronoun has in the sentence. Objective pronouns like me cannot be used as the subject of a sentence, and subject pronouns like I cannot be used as the objects of prepositions or as direct/indirect objects in a sentence. Always check your sentences carefully to be certain you have used the correct pronoun in the sentence for the function you have given the pronoun.