Continuity mistake: Toward the end of the film when Sam reaches the gate from which Joanna and her mother are departing, he looks down to see them in the boarding line with several people behind them. When he races down to say goodbye, Joanna is last in line.
Character mistake: The Christmas card to the Prime Minister from Natalie misspells Christmas - the "r" is omitted.
Factual error: When Billy Mack hears he is No. 1, the DJ, (Radio 1's Wes, who does the chart in reality) says the two singles which could be No. 1, then announces Billy is and plays it, without playing the no. 2 song first. The chart is done as an uninterrupted countdown, so even if it's known what no. 1 will be, they'll still play the "losing" song before it.
Suggested correction: In this instance, the DJ broke with protocol.
Revealing mistake: This is really a reverse mistake resulting in NON-visible crew. When the U.S. President's black limo arrives and stops so that the camera is facing the car's left rear side, you can see that the car has been smeared - unevenly - with some sort of gel to prevent us from seeing the reflection of the lights, crew, and the set opposite Downing Street.
