Factual error: When Ray cuts in front of a woman at the ATM, she runs to get a cop. She comes back with Robert. The problem is, Robert is a New York City cop, and Ray lives in Nassau County, which is not in New York City. Robert has no jurisdiction, and would not be patrolling in Nassau County.
Continuity mistake: Prior to bringing Ray up for the role-playing exercise, the parenting teacher erases a circled phrase from the chalkboard. Throughout the scene, the chalked circle flips several several times between being totally erased and having a faint outline left over.
Continuity mistake: Marie comes over with a cake shaped like a cross. In almost all the scenes where the family is sitting at the table different pieces of cake are missing. In some of the camera angles there are no pieces of cake cut from the bottom yet when the cake is seen from other angles there are.
Other mistake: When Amy runs out of the basement wearing Robert's pants, the pants are at full length, with the belt under her arms and the bottom of the pant legs at her ankles. When she is standing next to Robert, though, it is clear that he would have to pull the pants all the way up to his ribs for the legs to be the right length on him. Also, the pants are unzipped and the zipper pull is hanging just below Amy's breasts. Since a pants zipper is usually just an inch or so above the crotch, Amy would not be able to pull the pants that high unless there was a 12" drop between the zipper and the crotch of the pants.
Continuity mistake: In the scene where Debra tells Ray her parents have separated and he laughs, later on in this scene he tells Debra that he got free candy from the broken vending machine at work. When Debra leaves the room, Ray starts taking more candies out his pockets and throwing them on the bed. Take notice of the position of the sweets on the bed. Now just after the close up scene of Ray scratching his head, look at the position of the sweets. Totally different. One or two are actually closer to the end of the bed, whereas in the scene before, they were more further on.