Continuity mistake: As the Queen is about to take the call from Tony Blair in the kitchen you can see in front of her a few plates of food and a chopping board with two cucumbers and a black handle knife. Near the end of the scene we see an overhead shot and there is only one cucumber and the knife has disappeared as well.
Continuity mistake: When Her Majesty drives into the river, there is no road to be be seen on the other side, and her car stops about mid-river. In the next shot, when walking from the car, she is very close to the bank on the other side, and in a following shot there is a road leading up from the stalled car.
Continuity mistake: When Tony Blair and the Queen leave his final audience in London to go for a walk they exit the double doors of the chamber in Buckingham Palace and walk down the narrow halls of Balmoral Castle in Scotland (not Buckingham) and then suddenly are on the staircase of Buckingham again.