Dick Van Dyke's accent has always been a constant source of amusement for us Brits, and the Americans may not have known any different.
The American perception of how we speak is interesting, and often wide of the mark.
If you watch Frasier, Daphne's 'Manchester' accent is unique, and although it has occasional northern hints, it is nothing like anything I have ever heard spoken there.
Similarly, when her brother Simon rocks up, his accent is not only nothing like any English accent, it is also nothing like hers, which is odd since they are supposed to have grown up together!
The 'Midlands' accent from the rocker character on Just Shoot Me is similarly a little off the mark, but does land near Ozzy Osborne's Brummie twang, so the Americans can get the gist.
Family Guy often rib the British, with characters having bad teeth (a common perception of Americans is that we all have bad teeth) and accents so far back you find yourself translating as you listen.