When Johnny is wrestling with Pegasus' mother in the party room, Pegasus' daughter is heard telling Johnny to stop and she sounds as if she is on the other side of the room. However, she is next to him and does not say anything until the end.
When Johnny is in the restaurant with Agent 1, he drains his glass of wine and agent 1 asks the waitress for another bottle, in the next shot there is a small amount in the bottom of the glass, yet moments later the glass is about a third full.
When Kate Sumner analyzes the face of Johnny with a video camera, the camera points about 1 meter above Johnny. In the following shot that shows Johnny from the front, the camera points perfectly to his face and a perfect image is displayed on the monitor in the back. In the next shot the camera points above the head again.
In the kitchen scene at the end of the film, Johnny chops a celery then closes the drawer with his hip. In the next shot, the position of the right hand chopping board changes and a knife appears between the two boards.
At the Swiss government fortress, the German designation for the "Vista Lounge" reads "Aussicht Zimmer", which is supposed to be a literal translation of the former, but it is not only a misspelling (it should read "Aussichtszimmer") but also a term nobody in the German-speaking word would use for the room depicted - "Aussichtsraum" or "Aussichts-Lounge" would be more appropriate. Also the German term for the "Conference Chamber" is misspelled. Instead of "Konferenz Saal" it should read "Konferenzsaal".
During the aerial shot before the MI7 meeting in London, the wording to the bottom right of the "camera" screen says "GEOCACHING". Geocaching is a hobby using GPS to find hidden items, not something which should be on this sort of camera readout.
During the chase in Hong Kong, when Johnny English walks off the pallet after having been craned between buildings, he says Thank You to a builder in Mandarin. His experience should have told him to use Cantonese instead. However, as we saw in the first film, English is highly incompetent in many ways and this may be another.
Simon Ambrose informed the team that Johnny English is the third man in Vortex, resulting in the latter being suspended from the case. Why aren't they suspicious about Ambrose letting him stand in for Pamela?
When English visits Tucker at his home, and Tucker is playing a racing game on his laptop, the movements of his car in-game seem to have nothing to do with his actions on the keyboard. When he then stands to close the curtains and talk to English, the car continues to behave as if being controlled, showing that it's just a demo video.
The goof item below may give away important plot points.
Near the end of the film when Johnny English goes into spasm, he drops his pistol. Briefly, you can see stamped on the side 'Tokyo Marui', 'made in Japan'. This is a replica BB gun, and fairly harmless.