The most significant effect of different pronunciations of English due to dialects and varieties of English is that the debate over the correctness of English pronunciation is shifting away from a prescriptive assertion of the correct pronunciation toward a descriptive perspective that acknowledges that language speakers accommodate languages and dialects of languages that are in proximity and as a result will absorb features of the one language or dialect into the other. This linguistic feature of language is one of the factors pushing the debate over correct English pronunciation away from prescriptivist assertions and toward descriptivist acceptance.
The effect of this shift on the modern day world has been the development of a lenient acceptance of differences as the debate over prescriptive propriety has faded to descriptive acceptance. As an example of such accommodation, the proximity of Hindi to the Indian English variety has influenced the English th to move from a fricative pronunciation to a plosive pronunciation. One factor propelling this acceptance of these pronunciation differences is that the numbers of speakers of varieties of English is skyrocketing because English is often the language of education in countries where English is a national language, examples of this are India and Malaysia.
Pronunciation is a signifier of many kinds, in English, and, no doubt, in many other languages as well. Pronunciation can tell us what region of the United States a person is from, what generation a person is, what a person's socio-economic origins are, where a person was educated, sometimes where a person's parents were born, whether English is a person's first language, and if not, where the person learned to speak English.
We use this kind of information in various ways. Pronunciation is often used by law enforcement, for example, by the FBI, to gain useful information about a person of interest, maybe where that person was born or is likely to flee to. We use pronunciation to make judgments about a person's level of education or origins. Sometimes we can tell when a person is under stress, for example, if a person has acquired a newer regional accent and then reverts to earlier pronunciation habits.
One way pronunciation should never be used is as a judgment about a person's intelligence. People's pronunciations are absolutely not an indicator of how intelligent they are. And given how many English speakers there are all over the world, all pronouncing English in different ways, I should also say that, within limits, it is not a good idea to make judgments about what "correct" pronunciation is. A person from the Southern United States has very different pronunciation from a person in New England and neither is wrong in any way.