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)
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)
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)
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)
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.