I thought it was strange. I've no complaints about Helen Mirren's acting , she was excellent.
However, I was left wondering why it was called 'The Queen' as it seemed to be much more about Tony Blair on the one hand and Princess Diana on the other.
It seemed that three possible films were fighting to get out of the one movie: one about the Royal Family (old style); one about Princess Diana as an icon; and one rather inadequate political satire about Blair.
My main problem with it was that it was conspicuously ahistorical: it showed a Blair behaving as he now does (he has changed significantly in the same way Thatcher did, IMO); a Queen already diminished and made tragic by the Diana fiasco; and an already saintly Diana rather than the (by then) much maligned character who had become tabloid fodder.
Interestingly, in the trailers they showed The History Boys, and there was a quote which said something like 'there is no period so remote in history as the recent past'. This appeared true of The Queen.