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. (01:05:05 - 01:06:00)
Visible crew/equipment: After the Queen's jeep is stuck in the river, she glances around for a moment. The rigging of the lights and camera can be seen in the reflection of her glasses. Further, when she exits the car, the reflection of a man holding his hand to his chin can be seen in the door window. This must be a crew member, as in the next wide shot the Queen is completely alone. (00:59:50)
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.
Audio problem: At the very end of the movie when Tony Blair and Her Majesty are walking in the garden with the dogs, the audio of Blair's voice does not match his mouth. At some points his mouth is not even moving at all, yet we still hear the audio.
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.
Factual error: There's a scene where Tony Blair, in the back seat of a car, makes a phone call from what looks like a Nokia 6210 - a phone which Nokia didn't introduce until 2000, at least two, and possibly three years after the movie was set.