I have never had any trouble with other English accents other than accents of people for whom English is a second language.
I have had people have trouble with my, rather broad, Australian accent, however.
You may be able to pick an NZ accent easily but people who aren’t familiar with Australian and NZ accents can have trouble distinguishing them. I used to have trouble telling the diference between an Australian and South African accent. I still have trouble distinguishing between well spoken Australians and mild accented NZers.
To add an anecdote, I remember watching a BBC documentry about inner city poverty in the US on PBS. They interviewed some kids (from East LA I believe, it’s been a while). The interview was sub-titled. (Of course, it could have been that they were interviewing kids for whom English was a second language, but I don’t believe that was the case).
Take care,
GES
I lived in a town with a fair number of Ozzies, Kiwis and South Africans. It was a small town so you got to know most of the people in it. An urban or eastern (I’m sure I’m mucking this up) Aussie accent is still tough for me to distinguish from a Kiwi’s accent. South Africans, on the other hand, are a piece of cake. And don’t I love that accent of theirs.
It’s interesting, though, that I grew up in SoCal without any accent whatsoever. I enunciate perfectly at all times and speak the President’s English. Well, maybe not his English. 