Factual error: The opening scene shows Donna graduating from New College in 1979. That is not possible, women were only first admitted in 1979.
Continuity mistake: After young Donna and Bill are swimming back to the boat, Donna climbs up into the deck wearing a full face mask. In the long shot we see her turn around still wearing the mask. In the very next shot she sits down but the mask has vanished completely.
Factual error: Donna graduated in 1979. Assuming the events of the film took place in one year thereafter, Sophie would have been born in 1980. This film takes place five years after the events of the first film (where we know Sophie was 20 years old) so we would assume it's now 2005. Sophie and Sky are both seen talking on smartphones, which had not been invented yet.
Revealing mistake: After young Donna and Bill are swimming back to the boat after what is meant to be a beautiful ocean swim, Donna climbs up into the boat. In the high shot we can see a line or seam in the floor under the water that gives away it's being shot in a pool.
Continuity mistake: Young Donna has brown eyes. Older Donna has blue eyes.
Continuity mistake: When Donna begins to sing "Andante, Andante, " the camera shows Sophia, Bill's great-aunt and owner of the farmhouse, turning to the bar counter and setting down a rag. A few shots later, she is turned back to her original position and the rag is not there.
Continuity mistake: When Harry is tied to the chair - his method of problem solving - there is a small boat tied up directly outside the window. Seconds later when he falls out the window into the water, the boat has vanished.
Continuity mistake: When young Sam is rowing young Donna the starboard oar shifts position from aft of the oar pin to fore, then back aft.
Continuity mistake: When Sophie greets Rosie and Tanya at the dock and hugs them both, Sophie's arm is under Rosie's arm in the shots facing the boat, but in the shot facing Sophie her arm is around Rosie's shoulders.