MoonstruckGoofs
Continuity
When Loretta tells Cosmo she is getting married, the wine glasses and bottle do not match when the camera cuts from Loretta to Cosmo.
During the breakfast scene, Cosmo's (Vincent Gardenia) eyeglass frames change from one style to another after his father sits down.
At the end of the movie, Rose's hairstyle changes between shots as she goes to answer door.
Factual errors
Loretta says "ti amo" to her father, and he answers "ti amo." "I love you" is the accepted English translation, but "ti amo" refers only to romantic love, and would never be used between father and daughter. They would say "ti voglio bene" instead.
When Loretta is leaving Ronny's apartment after saying she would go to the opera with him, he says to meet him at the Met. She comes back and asks "Where's the Met?". She took a cab, which of course would know where the Met is.
Incorrectly regarded as goofs
Ronny and Johnny Cammareri's mother lives in Sicily, even though they were clearly raised in the United States (they have American accents and an established business in Brooklyn). This is perfectly possible -- their mother likely married an American and then moved back to Sicily after he died (that's exactly what my grandmother did after my grandfather passed).
Loretta is about to marry Johnny Cammareri, and yet she has never been to his bakery and never met his brother. However, this is not impossible -- Johnny could have divested himself from the business after he and his brother fell out. There's no indication in the story that Johnny is involved in the bakery (it could have been named Cammareri Bros. Bakery at an earlier stage, when he and his brother were still on good terms).
So if he isn't involved in the business, and didn't want to talk about his brother in general, it's perfectly possible that Loretta would not go there or even know he had a sibling.
Revealing mistakes
Loretta's grandfather enters the kitchen with dogs in front of him. As he walks through, you can see a leash pulling the dogs from off camera.
When Ronny demands that Loretta comes to bed with him, she reaches out to hold his artificial hand, and his thumb moves.
In the opening moments of the film, the 'corpse' in Nucciarone's Funeral Parlor can be seen swallowing, the skin of his neck moving.
Miscellaneous
When Johnny visits Rose late at night, she opens the door for him, Johnny walks in, and no one closes the door. Later, the grandfather walks in with his dogs and closes it.
Audio/visual unsynchronised
When Loretta is talking to Cosmo in the kitchen, we hear and see her tearing at the capsule on the wine bottle. In the next shot, we can still see the bottle and hear the tearing, but Loretta's hand is not there.
Errors in geography
Loretta and Jonny leave the Grand Ticino restaurant, seen as being on Hicks St, which is in downtown Brooklyn. Loretta drives Jonny to the airport for his flight to Sicily, traveling via a tunnel. Since it's an international flight, he'd be going to JFK, but there's no need to travel via a tunnel from Brooklyn to JFK.
Boom mic visible
In the final scene, when Rita and Raymond show up, a boom mic is reflected in the glass in the cabinet.
Character error
Early in the movie, Loretta greets her grandfather as he comes down the stairs, but she says "ciao, bella," which is to greet a woman. She should have said "ciao, bello."
While at the opera during intermission, Cosmo orders a Canadian Club and ginger ale, and a Dubonnet on the rocks. While he and Mona are drinking, the C.C. and ginger ale isn't being drunk by either of them. Cosmo is drinking the Dubonnet, and Mona is drinking red wine.