Factual error: At the ball, in 1957, they play Eddie Cochran's "C'Mon Everybody" which wasn't written until 1958.
Continuity mistake: When the girls call 'hello' to the butcher, he is standing in the doorway of his shop holding a cleaver with his assistant behind him. The angle changes and the assistant is now beside him and he has both his hands in his pockets.
Continuity mistake: Jack's tie changes between the time the 3 girls meet him on the way to the first lecture and when we see him in the lecture itself. In the first scene it is all dark, in the 2nd there is a light stripe below the knot.
Other mistake: When walking home from the cinema, Sean says to Bernadette (played by Minnie Driver) "I think your father would be very disappointed to hear that, Minnie". Yes it is Bennie the first time (her character's name), but the second time (ie. the sentence above) is definitely "Minnie".
Continuity mistake: At the end, when Jack returns to Benny in her shop, she wears her hair in a ponytail. In the shots of him talking, her hair covers the top part of her ear, but in the shots of her, it is behind her ear completely.