I've picked up some British slang just from context. So this wasn't all new to me, though there were a few surprises, particularly the compilers' own perception of of American usage, perhaps that's due to limited exposure to some friends who are not familiar with all expressions.
What could have been left out
I never thought of DIY as a British term; it's one Americans use regularly.Also most Americans (apparently, excluding the friends of the compiler) understand that "piece of cake" means that something is easy, though some, for some reason prefer the term "cake walk." You could also say "easy as pie" here, though I don't know if they would get the gist of that over the pond. .
We also say "haggle" and are not too likely to say"dicker."
Also Americans tend to say "excuse me" both for things like burping and to suggest that someone move out of their way far more often than "pardon me," so the distinctions the list presents are not exactly accurate.
Oh, and some of us do use the -ly ending for adverbs, thank you very much!
What could have been included
terms like "brill" is mentioned in passing, though it doesn't have its own entry. It could have been included because the word "brilliant" does have different connotation in British usage than in American usage. Over here, people use it primarily to mean really smart but not as the equivalent of "terrific."
Other regional differences?
Perhaps it has something to do with focusing on strictly English slang rather than some that may extend to other parts of the UK. Here's the entry on "cracking" -"If something is cracking, it means it is the best. Usually said without pronouncing the last "G". If a girl is cracking it means she is stunning." From what I recall there's another slang meaning for "crack," though that may be more strictly speaking Irish usage. It appeared several times in a novel I once read and clearly meant talk, chat, of the variety one expects to have in a pub.
Still it's an entertaining read.