Are there any mutually unintelligible English dialects? So far I've only been able to learn is that English is highly intelligible among its different dialects, but no actual statement that all dialect are mutually intelligible.
Two considerations need to be taken into account, I think. One is accent/pronunciation. The first time I saw Letter to Brezhnev, a 1985 film set in Liverpool, I repeatedly wished during the opening 20 minutes or so that the film had included subtitles because I found it so difficult to understand what the actors were saying. But after a while, I got used to the (consistent) differences in pronunciation from what I was accustomed to hearing, and I could understand most of the dialogue quite well the rest of the way.
The second consideration is vocabulary. To the extent that a dialect incorporates multiple unknown words, it is impossible to fully comprehend speech in that dialect unless you can look up the unknown words or ask the speaker what they mean.
Here is a quotation I recently encountered from James Hogg, The Three Perils of Man; or, War, Women, and Witchcraft (1822), spoken by a farmer who lives on the border of Scotland and England:
"Bessy Chisholm—Heh! Are ye therein? May Chisholm—where's your titty? Poor tafferel ruined tawpies! What are ye gaun gaindering about that gate for, as ye didna ken whilk end o' ye were uppermost?"
I would venture to guess that very few English speakers could accurately translate four of the words that appear in close proximity in that excerpt—titty, tafferel, tawpies, and gaindering—and many might also have trouble with "didna ken whilk."
An English speaker would surely recognize the wording here as being (from their perspective) "mostly English"—but if several crucial words in a small amount of space are unknown to the reader, the sentence is, for practical purposes, unintelligible. And as goes the sentence, so goes the dialect.