Continuity mistake: During the night scene when the cop is shot, the cigarette in Peter Stormare's mouth switches between being long and nearly consumed. (00:28:52)
Continuity mistake: In the scene when Jean is having a talk with Scotty about his grades and not wanting him to go out for hockey, the phone rings and the camera focuses on Jean and the phone. The microwave clock behind her reads 10:44. Jerry then enters the scene to talk on the phone and the shot reverts to Scotty shouting the obscenity then back to Jerry and the microwave clock now reads 7:43. The shot moves back to Scotty with him shaking his head and then back to Jerry where the microwave clock now reads 11:05. (00:12:35)
Continuity mistake: When Margie is in Jerry's office for the second time and Jerry rushes out to "count the stock", Margie looks at his wife's photo and it seems the photo is just in front of her as she doesn't turn around. When Jerry flees and she stands up, we see the photo is just behind her, under one of the golf player statues. (01:22:50)
Continuity mistake: When driving from Brainerd to Mpls, the bad guys are seen driving north on I35...which means they passed the cities on the drive back from Brainerd.
Continuity mistake: When Margie and her husband have lunch in Margie's office, the bag of nightcrawlers on the table changes position several times during the scene. (00:45:36)
Continuity mistake: When Carl comes back from the ransom collecting and quarrels with his partner, the Esmeralda mug on the tray keeps changing position during the scene (watch the Esmeralda image and the ear of the mug). (01:23:31)
Continuity mistake: In the opening scene when Jerry talks to the two kidnappers, the beer bottles on the table keep changing their position. (00:04:04)
Continuity mistake: When Margie visits Jerry for the first time, her scarf changes position from shot to shot. (00:59:36)
Continuity mistake: After the one guy shoots the cop, a blue Ford passes them. So the bad guy goes after them to find that the Ford flipped over. He stops then puts the Oldsmobile in reverse. Just before the car stops you can see that the taillights are from a 1989 or 1990 model. The film is set in 1986 or 1987.
Continuity mistake: The pistol used by Marge to shoot Gaear on the lake changes between camera shots. Look at the length of the barrel as she points the gun at him after he runs off, and then compare it to after she has shot him and points it to the ground. The pistol first seen is a snub nose .38. The second shot shows a "Patrolman" .357 Magnum. (01:29:00)
Continuity mistake: When Margie eats lunch with her husband in the office, the hamburger she holds is alternatively untouched and bitten. This is the most evident when she talks to her colleague about the car. (00:45:48)
Continuity mistake: When Marge sees Gaer shove Carl's body into the wood chipper, there's a huge blood puddle around the wood chipper. But moments later, as she shoots runaway Gaer, the wood chipper is visible behind her and the puddle completely disappears. There are only minor blood stains.
Continuity mistake: When Shep strangles Carl with the leather belt, as he is putting the belt around Carl's neck Carl's hands are caught inside the belt as the shot changes; but when the shot changes to a different angle his hands are seen outside the belt.
Continuity mistake: When the cop is shot in the head, no blood splatters onto Steve Buscemi's face, but there's blood on it in the very next shot.
Continuity mistake: When Steve Buscemi is shot in the cheek, he touches the wound, and in the first shot there's no blood on his hand, but in the very next shot there is.
Continuity mistake: When Marge goes back to Lundegaard's office for the second time, he is working on writing the vin numbers on a paper on a clip board, scratching them off and scratching his pencil on a "I love golf" notepad. When he leaves his office to complete a "Lot Count", Marge is looking around Lundegaard's office. The camera pans back to his desk and the paper that Lundegaard was writing the vehicles vins on the clipboard is no longer there and has been replaced with another piece of paper/application.
Answer: While there is nothing in the film that explains this, the most likely step taken by the authorities would have been to see whether Jerry and his wife had made out an will and who they would give legal custody of their son if anything happened to them. If there was no will then it's likely the closest family or relatives would be asked to take custody.
Lummie ★
He probably still has Lundegaard Grandparent (s) and a grandmother from his mother's side - any of which could and would become his legal guardian (s).
KeyZOid
He'll be a rich man. Grandfather said early in the movie that his daughter and her son would bever have to worry about money or words to that effect.