Learn Spanish (Latin America): Nuestros abuelos hablaban distinto y el dialecto iba cambiando. - Our grandparents spoke differently, and the dialect was gradually changing.

While estaba cambiando just states the past action in progress ('was changing'), using ir + gerund emphasizes that the change was gradual and happened little by little. Iba cambiando translates closer to 'was gradually changing' or 'kept changing step by step'.

Could I use venía cambiando here instead?

Yes, but the perspective shifts slightly. Iba cambiando describes a gradual change moving forward from a point in the past. Venía cambiando (using venir + gerund) implies the change started further back and progressed up to that point of reference, feeling closer to 'had been gradually changing leading up to then'.

Why does the sentence use distinto instead of the adverb distintamente?

In conversational Spanish, it is very common to use the masculine singular form of certain adjectives as an adverb to describe how an action is done. Saying hablaban distinto (they spoke differently) is completely correct and sounds much more natural than adding the -mente suffix.

Why are both hablaban and iba in the imperfect tense?

The imperfect tense is used because both actions were ongoing, continuous background situations in the past. There is no specific beginning or end point mentioned for how the grandparents spoke or how the dialect evolved.