Learn Russian: Почему мне надо постоянно исправлять твои ошибки? - Why do I need to constantly correct your mistakes?

After modal words like надо, the choice of aspect depends on whether it is a repeated process or a one-time result. Because of the word постоянно (constantly), this is a repeating, ongoing action. Therefore, we must use the imperfective infinitive исправлять.

Why does the sentence use мне instead of я?

In Russian, words expressing need or necessity like надо or нужно do not take a normal subject. Instead, the person who "needs" to do the action is put in the Dative case. So, "I need" becomes мне надо (literally "to me it is necessary").

Are твои ошибки in the Nominative or Accusative case?

They are in the Accusative case, since they are the direct object receiving the action of исправлять (to correct). For inanimate plural nouns (things that are not alive), the Accusative case looks exactly identical to their Nominative dictionary form.

Could I use нужно instead of надо in this sentence?

Yes! When followed by an infinitive verb like исправлять, надо and нужно mean the exact same thing and are completely interchangeable.