Helen Mirren's tattoo at the base of her left thumb is clearly visible when she is holding a newspaper. This can be verified in the IMDb photo gallery for 'The Queen'. Elizabeth II is not likely to have the same tattoo.
When Tony Blair is riding to the airport in the back of his Jaguar, in the background you can see a Mercedes Benz S-class with an 02 number plate (ie March-August 2002). There also appears to be an out-of focus 52 plate (September 2002-February 2003) later in the same scene. At this point in the film it is 1997.
In the first scene where Blair is talking to the Queen, when she puts down the phone he hears the old pulse dialing tone, this was phased out by BT, in London, long previous to 1997 when the film is set.
While in the back of his car, Tony Blair takes a call on his mobile phone from the Lord Chamberlain. Blair's handset is a Nokia 6210 which was not released until 2001 (four years after the film was set).
When Tony Blair was on his way to the airport, three cars in the background were out of place. First, there was a W220 Mercedes S class. The W220 model was produced from late 1999 to 2006. Later, you can see a second generation Nissan Almera passing in the background. That model was produced from 2000 to 2006. Finally, a second generation Toyota Rav4 was seen passing. That model was produced from 2001 to 2005.
When Tony Blair is riding to the airport in the back of his Jaguar, in the background you can see an aerodynamically designed Toyota Rav4. This design was introduced in 2001. Prior to this, all Toyota Rav4's had a distinctive rectilinear design.
In both Government offices and Royal residences, many examples of the old-fashioned 'dial' telephone can be seen in use. These were generally phased out by the mid-1980s so it is highly unlikely that so many would still be in use in 1997, when the film is set.
When the Queen gets in the green jeep with Charles to go stalking (the stag) she loads up 2 black Labrador retrievers. When she stops the vehicle and says she'd rather walk back, she opens the door of the vehicle to take the dogs with her, and 3 black Labradors get out.
When the Queen drives into the river and the car gets stuck we see that on the other side of the river there is little to no road and lots of heather. When later there's a shot from above, the car is suddenly facing the side of the river where the road is clearly marked, and the heather covered bank is now behind the car.
In the scene before the Queen addresses England, she is advised to make the change "and as a grandmother." She writes the correction, clearly caps her pen and begins putting it back. In the very next shot, she caps the pen a second time.
When the Queen and Prince Charles are set for a drive, Queen Elizabeth is wearing her glasses as she puts the Rover in gear and drives off. Cut to a different angle (from the front of the Rover) and her glasses are nowhere in sight.
In the first audience scene with Tony Blair, the Queen uses a bell (on the table next to where she was sitting) to let the footman know to usher in Mrs. Blair. In the final audience scene, the same table is bare. Frears and Morgan themselves point out this goof in their commentary on the DVD.
When the Queen is being driven to Princess Diana's funeral, we see actual footage of her Majesty's specially modified Rolls-Royce Phantom V (with a raised roof and large rear windows), when we see a close up of the Queen (Helen Mirren) in the Rolls-Royce, it is a standard (unmodified) model.
As Tony and Cherie Blair watch the Queen's televised address to the nation, the Prime Minister remarks to his wife that what the Queen is doing is extraordinary; as he says this, he's pointing at the television screen with the forefinger of his left hand; in the next shot, a wider-angle two-shot of the Blairs, he's pointing with the forefinger of his right hand.
When the Queen walks toward the picnic area and calls to her dogs, four Corgis come running up behind her on the path and race past her. In the next shot, the Queen throws some scraps of food to her dogs and tells them to "stay". The four Corgis are seen sitting together looking back at her, but a fifth one can also be seen behind the Queen standing by Prince Phillip and the grill.
In the scene in which the queen disables her Rover in the riverbed and is stranded, alone, when she opens the car door you can very clearly see in the window the reflection of a man looking on from the shore.
When the Queen goes to see the trophy stag after it was shot only its head has been removed. A hunter would first have to field dress (gut) the animal where it lay and then immediately skin it once it was hanging. Also, the head was removed far too high up the neck; not enough of the cape was left for it to be mounted.
While the Queen does drive herself on her lands, her security is always at a discreet distance; it is inconceivable that she would have to call for assistance, much less, be allowed to be stranded like the average motorist.
When Diana's coffin arrives at RAF Brize Norton, a Marconi S511 radar is visible in the background. RAF Brize Norton employs a (rival) Plessey Watchman radar. A more likely location for filming is Southend Airport, UK.
After the funeral on Saturday 6th September, the film moves on '2 Months Later'. This assumes we are now on or around 6th November. The Queen remarks to Mr Blair that 'the clocks go back next week'. The clocks, however, went back on the 26th October in 1997.
The real Lord Airlie, David Ogilvy, 13th Earl of Airlie, was born in 1926, making him 71 years old during the events depicted in this film, the actor who plays him, Douglas Reith, is clearly much younger than this.
When in the film they mention that the Union Jack is not flying at half mast, they should have said "Union Flag" as the Union Jack is the name of the flag on a boat or ship. However, the British flag is colloquially known as the Union Jack, so whilst its correct title is indeed the Union Flag, the vast majority of the population call it the Union Jack irrespective of where it is flown.
Several people in the film repeatedly refer to the practice of flying a flag at "half-mast" to honor someone recently deceased, in this case at Buckingham Palace. Although in the US the term used is "half-staff", in the UK it is correct to say "half-mast", whether the half-mast flag in question is on land or sea, according to the Flag Institute.
The Tuesday meeting in the Chancellor's office is at 10 am, and Blair's aide returns to say it lasted "two and a half hours". Yet, back at Balmoral, it is morning and everyone is preparing to leave to flush the buck when the faxed memorandum reporting on the results of the meeting arrives.