Sup y'all. I have a master's in sociolinguistics.
Obviously people in here have suggested as much already, but language vs. dialect (vs. accent) is primarily a sociopolitical distinction, not a technical one. Linguists tend to use "variety" to skirt around that debate. In terms of varieties of English being homogeneous: not especially or anything! English is, in spite of the media apparatus that broadcasts it to every corner of the planet, still diversifying, and rapidly. Even just within the United States, African American English is a massive, flourishing variety with its own phonology and a very distinct set of syntactic and morphological rules. If there is one remarkable thing about English here, it's that it has a very consistent consonant inventory across varieties in a way that a lot of languages don't. Our phonetic variation is generally restricted to vowels, which helps English speakers understand each other.
We also have to think about this diachronically (across time). Many varieties of English, especially American varieties and global Englishes, came into existence relatively recently, so they haven't had as much chance to diverge. It's not at all impossible that some varieties may continue to change to such an extent that they'll begin to lose their intelligibility to non-speakers. (And yes, naturally you can give it a thousand years or so and end up with entirely new languages a la Latin--it's the linguistic circle of life, baby!)
