Continuity mistake: When Donna is fixing the crack in the tiles, the tip of the filler-gun breaks off. She stands up, and a bit later waves the filler gun, with the tip back on. The pistol has been out of sight (her hands down) during the scene, but she didn't look down once, and we see that she is carrying a bowl in the other hand, so she would not have had a chance to put the tip back on again.
Continuity mistake: When Sky is getting his hat and cigar as "props" for his stag party, as he leaves the room wearing the hat and holding the cigar. In the second shot as he walks past Sophie, there is a long loose cord hanging down from the brim of the hat - which wasn't there in the first shot. (00:10:00)
Continuity mistake: At the chapel, Sam has just proposed to Donna. She says she's not a bigamist. Sam says neither is he and that he has loved Donna for the past 21 years. To his right stands Sophie, who after hearing Sam say this, is all choked up and looks like she's about to burst into tears of joy. Immediately after you see this expression we see Donna very briefly (one or two seconds). When the shot goes back onto Sam and Sophie, Sophie has a huge grin on her face. Nothing is said by Donna or Sam in this extremely brief period of time that would justify her instantaneous change of expression.
Continuity mistake: By the end of the song "Chiquitita", Donna has a red rose in the side of her head (positioned in her hair) after Rosie put it in there. As the shots differ, in some shots the red rose, which should be visible (judged by the amount of the side of Donna's head we can see), is not there. It appears and then disappears a few times and is not due to the angle. (00:32:10)
Continuity mistake: When Donna climbs on top of the goathouse after seeing Sam, Bill and Harry, and begins to sing "Mamma Mia", as she rolls around all over the roof her dunagrees (especially the knees) become dirty. However the amount, prominence and position of the dust and dirt on her clothing changes a few times during the whole scene. (00:26:10)
Continuity mistake: When Donna, Tanya and Rosie are on the couch talking, Tanya asks Donna "if she's getting any." As she asks her this, the shot switches angles. And as it does, the towel that Tanya is wearing on her head changes from dangling behind her shoulder to suddenly hanging in front of it. (00:21:50)