Continuity mistake: When the family turn off the museum electrical system and then run away, their shoes are dry and do not leave wet footprints on the floor. Only when Millicent checks the electrics do the footprints appear.
Plot hole: While on the boat, Paddington suddenly appears inside the mail sack, thus implying he managed to open the precinct, get inside the sack and find someone who closed the precinct again. An impossible task.
Continuity mistake: In the classic bathroom scene, the bath is seen to start rising from an underwater perspective. The bath has very firm, large, and securely held on feet, and yet they disappear by the time the bath hits the stairs.
Continuity mistake: Just before the wallet thief smashes up the green VW Golf, there is a shot where you can see that the hubcap is missing from the passenger side front wheel. In a later shot however when it shows the VW Golf has come to a rest, the hubcap is now back on.