Continuity: After Ted gets mad at Billy for eating ice cream instead of dinner, he carries him from the kitchen into the living room and the spoon in Billy's hand disappears.
Continuity: Ted's job interview takes place at 4pm during the office Christmas party, but outside the office window Manhattan is bathed in bright mid-day sun.
Continuity: When Ted is first making French Toast, he picks up the egg in his right hand; when he shows it to Billy before breaking it, it's in his left hand; when the camera goes to closeup as he breaks the egg, it's back in his right hand. Dustin Hoffman's disheveled hair also changes wildly in that scene.
Continuity: When Billy is waiting for Ted to fetch him after the birthday party, he sits on the chair with his left leg tucked under the right leg. In the next shot, his right leg is tucked under his left leg.
Factual errors: When Ted is showing his portfolio, there is a view of Central Park from the window. The scene takes place around Christmas time, but there are still leaves on all the trees.
Errors made by characters (possibly deliberate errors by the filmmakers): When Ted is interviewing for his new job, he is told that it is the Friday before Christmas, December 22. In 1979, when this movie was released, December 22 fell on Saturday, not on Friday.
Revealing mistakes: There is a scene of Billy on stage at his school's Halloween play, which presumably takes place in late October. In two outdoor scenes immediately following, Ted and Billy are in Central Park, and Ted is dropping Billy off at school. In these two scenes, trees are in full bloom and green. At that time of year in New York City, the tree leaves would have certainly changed colors and begun to fall.
Continuity: After Ted throws the wine glass at the wall, Joanna goes from having one hand at her jaw to having both hands.
Continuity: The position of Phyllis' hands change several times when she is in the hallway naked.
Continuity: After Ted drops Billy at school, Joanna's hand position on the window changes between shots.