Continuity mistake: At the beginning of the episode, it is the middle of the night when it shows the first shot of The Drunken Clam. This is at the very beginning of the episode and not the first scene after the opening titles by the way. But after Cleveland says he lost the house to Loretta in his divorce, Quagmire asks him where he is going to live. Cleveland replies by asking Quagmire if he can stay at his house. When he says this, it is now the middle of the day. You can notice this from all the other open windows in all the other booths, revealing the daylight. (00:00:05)
Continuity mistake: When Peter launches himself off a firework into Cleveland's house he hits the top floor and completely misses the ground floor. Yet the entire house is damaged including the ground floor. (00:01:25)
Other mistake: When everyone is saying goodbye to Cleveland and Cleveland Junior, they are standing next to Cleveland's house. Then after they have left and Stewie says "What the hell? He's getting his own show?!", they are standing next to Peter's house. Cleveland's house however, is across the street from Peter's house and could have not been able to stand next to Peter's house if they are at Cleveland's house. (00:03:20)
Continuity mistake: When Cleveland is trying to convince Donna to be with him, it is the middle of night. But as Cleveland and Donna kiss and the camera pans round, daylight can be seen outside the window. (00:19:55)
Da Doggone Daddy-Daughter Dinner Dance - S1-E2
Continuity mistake: When Cleveland drops Cleveland Junior off at school, Junior gets out at the back of the car and he is taller than the car's height. In the next shot, he is standing at the front of the car without enough time to move there and he is smaller than the car's height. (00:01:40)
Other mistake: Lester's house is directly across the street from Cleveland's. However, when the Child Services agent runs out of Lester's house with Ernie, he runs at 2 o'clock direction (which would be towards Holt's house), but instead ends up in front of Cleveland's house, which is in a 12 o'clock direction. (00:11:20)
Continuity mistake: At the start of the meeting, Ernie is wearing no socks. But when Lester says "I ain't leaving with out my son", Ernie suddenly is wearing socks. (00:17:15)
Continuity mistake: When Cleveland and the Child Services agent are hiding behind the couch during the gunfight, the bullet holes in the wall next to them change position between shots. (00:18:45)
Continuity mistake: When everyone is having breakfast and Donna tells everyone to make their beds, Donna is standing straight. However, in the next shot Donna is now slouching. (00:01:00)
Continuity mistake: When Cleveland is doing his Mini Mall rap, there is a shot of him next to a bed and wardrobe. However, when the shot zooms out, next to him is now a mirror. (00:02:25)
Continuity mistake: When Cleveland, Tim and Terry are at the Broken Stool, in front of them are empty beer glasses and a top hat right next to the glasses. However, when it shows the shots of Cleveland and Terry, the top hat is now several inches away from the glasses. (00:12:00)
Continuity mistake: When Terry crashes the van into a lamp post, the wing mirror smashes. But after Cleveland has his flashback and Terry looks into the wing mirror to spot the police, the wing mirror is now intact. (00:13:05)
Revealing mistake: After crashing the van into a lamp post, Terry looks into the wing mirror to spot the police. However, when he gets out of the van, you can see that the angle of the mirror would make it impossible to spot the police in relation to the van's position. (00:13:35)
Audio problem: In the final scene when Cleveland says to Terry "I'm gonna get paid and you're gonna get laid", they both start cheering. But when it comes to the wide shot, Terry is still cheering but his mouth isn't moving. (00:19:55)
Cleveland Jr. Cherry Bomb - S1-E5
Audio problem: When the audience is applauding Cleveland, applause is heard but no-one's hands are moving. (00:04:05)
Other mistake: Donna's friend Yvette stabs a man's hand with a knife when his hand was placed on a table. Yet no damage is made to the table. (00:11:30)
Continuity mistake: Cleveland takes the photo album off his dad and his dad gives him the dirty look. Cleveland drops the album but disappears in the wide shot of people fighting. (00:04:45)
Continuity mistake: Roberta goes to leave the house and she starts a tug of war with Donna. They are standing next to the door in this shot, but standing next to a table about 15 seconds after. (00:04:45)
Continuity mistake: Cleveland smashes a bottle to defend himself with. In the wide shot, all of the smashed glass disappears off the ground. (00:04:55)
Continuity mistake: Cleveland drops a spoon Junior throws at him. It disappears a few seconds later. (00:04:55)
Answer: In the episode "A Rodent Like This" Rallo discovers that Cleveland Jr. is actually a secret agent who is tracking down Tim, who is actually criminal. Jr. reveals that in order to get close he had to eliminate the real Cleveland Jr. luckily Cleveland doesn't pay attention so it was easy. Whether or not this is canon or not depends on the writers.