I only made it through A, B, and C, before I got tired of it, but in just those letters I came across quite a few surprising ones. There are lots I didn't really care about, or which seem clear enough from context, but there are a fair number of words which could be used in the same context but mean something different!
I knew that "chips" were different foods in the US and the UK, that "buzzards" were different birds, and that "awesome" and "brilliant" had rather different senses.
Some of the words I should have known, but didn't: apartment, asian, athlete (athletics), biscuit, bureau, candy, cookie, cowboy, davenport, and (police) commissioner. With each of these, it would be easy to have a sentence in one dialect which has a perfectly reasonable and significantly different meaning in the other dialect. Actually, I had some sense of confusion about "apartment", "biscuit", "bureau", and "davenport", but I hadn't realized it was just a British vs. American thing.
With some work, one could probably make a pretty good LJ poll around this.
(I'm reminded of my first stay in Ireland, some years back, when I was told that the unit of currency (in those days, the Irish Pound, sometimes written "punt") was pronounced to rhyme with "bank manager". I got the joke, but was somewhat surprised (even though the president of Ireland was then a woman) that managing banks was seen as a woman's job. This table corrects me about how that particular bit of slang is used.)
I have some professional interest in this because (a) I work with lots of non-Americans, and (b) I'm currently wandering around in "Extensibility Theory", where language conflicts like these ("false friends") are a particular danger to be avoided.)