Donna's first meeting with Bill, Harry and Sam take place in 1979. Sophie being 25 would mean that the present timeline of this film would take place in 2005 or 2006, which means the characters wouldn't have the technology of 2017, most notably the iPhone models that Sophie and Bill's mom possess.
While no specific dates are mentioned in the first movie, Sophie states in it that she's 20 years old, and Sam comments that he hasn't seen Donna in "over 20 years." The sequel ostensibly takes place five years later, with flashbacks to Donna's youth in 1979 and the birth of Sophie in 1980 (summer 1979 + nine months), which infers that the "present-day" scenes must be in 2005. However, multiple scenes feature technology contemporaneous with when the movie was filmed in 2017, including late-model phones with large touchscreen. Most noticeably, Bill is shown driving a Mercedes-Benz X-Class pickup truck to the airport in Stockholm; it was the manufacturer's first pickup truck, and it first debuted in 2017 for the 2018 model year.
The village band playing in a rural Greek bar/taverna in 1979 were kitted out with multiple hand-held radio microphones. Although they were first introduced in this year by Nady, professional international acts of this period were still using wired microphones and it is unthinkable a local group would be using these.
In the first movie Donna tells Tonya and Rosie that Sophie has three potential fathers because they didn't know bout Bill or Harry. However in the second both knew about Bill and would have suspected that there was an issue with paternity.
When Donna and the Dynamos sing 'When I Kissed The Teacher' in 1979 they are dressed in early seventies Glam Rock clothing and platform boots, a style which would have been extremely out of fashion by the end of the decade.
Among the many items of technology seen that would not have been available in the film's notional 2005 setting are the Microsoft Surface tablet/laptops used in the Japanese contract discussion scene. The first of these models only became available in 2012.
If Donna was 22 when she graduated college and got pregnant shortly thereafter and Sophie is 25 in present day, that would have made Donna, Tanya and Rosie 47 or 48 years old and Harry, Bill and Sam around that age, too. The actors are clearly older. Bill even states he's in his 50's in one scene.
While Bill's talking to his mother on the phone, they're both speaking English. However, both being native Swedish speakers, the conversation should've been in Swedish. While his twin brother's speech being in English, which could be justified as everyone present at the award ceremony might not be Swedish-speakers, the bit between Bill and their mother was a private conversation between two native Swedish-speakers. Hence, there would be no reason for them to be talking in English.
In the church scene, Donna appears in the form of a ghost that only Sophie can see. However, Ruby turns her head, looks directly at Donna from top to bottom and stares for a little before the camera switches.
The first movie establishes that Donna hooked up with her three suitors in the following order: Sam, the evening before July 17; Bill, the evening before August 4; and Harry, August 11. In the flashbacks of young Donna, she has sex with Harry first, then Sam, and then Bill.
During the Mamma Mia! sequence in Mamma Mia! (2008,) young Harry is shown with a bolted necklace, longer hair. Young Bill had long blonde hair and eye tattoo on his knees. Young Sam had long brown hair and a goatee. Mamma Mia!: Here we go again gave completely different looks to the new actors playing the young versions of the characters.
The events in both "Mamma Mia!" and the sequel take place primarily on the (fictional) Greek island of Kalokairi, but the outdoor scenes were visibly filmed in areas that look very little alike. While the original was filmed on location in Greece, on a heavily treed island, filming for the sequel took place in Croatia instead, on an island in what appears to be a much more barren climate.
In the first movie Donna says she didn't go back to America because her parents wouldn't have approved of her getting pregnant without getting married. In this movie her father was never in the picture and it is implied that her mom got pregnant with her after a one night stand.
In the first movie Donna sings the ABBA tune "Our Last Summer" to describe her Parisian romance with Harry. The song clearly describes an extended series of events, with lyrics such as, "We had our chance / It was a fine and true romance" and "I can still recall our last summer, I still see it all / Walks along the Seine, laughing in the rain". In the sequel, however, Donna spends only a single day in Paris en route to Greece, and also only a one-night stand there with Harry.
Upon young Donna's first visit to the barn, she slides down the banister and it falls apart along with the steps. Later that week upon learning about Sam's engagement she returns to the barn and breaks it off with Sam then storms up the stairs, which are now in tact only missing the banister.
During the number "When I Kissed The Teacher", Donna and the Dynamos' microphones disappear and reappear. They have the microphones at the beginning of the number but they disappear when they are crowd surfing. The microphones reappear after the biking sequence when the Dynamos climb on top of the boat towards the end of the number.
After the "Waterloo" sequence ends and the film returns to present day, Sophie leaves a sleeping Tonya and Rosie to go see Sam. When she gets up from the bed, she is wearing a blue striped shirt, but in the next shot when she arrives at Sam's, she is wearing a floral shirt.
During the 14th musical number Fernando, just after Ruby Sheridan (Cher) has said ''Fernando?'' the camera quickly switches to a distant view of Fernando (Andi Garcia) where you can see a crew member - wearing headphones - taking a fire torch off Fernando.
Donna says her mother's heart was broken after a romance in Central America. Ruby's romance with Fernando happened in Mexico in 1959. However, Mexico is in North America. At one point, she even sings about crossing the Rio Grande River into the US.
Toward the end of the movie, Sophie refers to Sam as her, "Step Dad," but throughout the story line, refers to all three men as her, "Dads," especially since one of them would be biological. Since Sam married Donna at the end of the first film, he legally, and actually, IS Sophie's Step-Dad, regardless of what their biological relationship is.