Ted gets mad at Billy for eating ice cream instead of dinner, he lifts him from the chair and the ice cream on the spoon in Billy's hand is missing, while a second before Billy was about to have a giant bite.
Ted Kramer's lawyer tells him that his ex-wife will meet him and their son at "the Central Park Boat Pond," but when the meeting actually takes place, it is at Literary Walk.
The position of Phyllis's hands changes several times when she is in the hallway naked.
When Ted is writing the "pros & cons" for his lawyer, a plate is at the upper left corner of the notepad, but it's not there in the distant shot.
Dustin Hoffman pours raw egg & milk mixture into the pan while making the french toast. Later the pan contents burn. The close-up shows it all as browning. After that close-up Hoffman drops the pan on the floor. The egg and milk mixture flies out, and it is raw again.
When Ted goes to apply for a job, the date is Friday, December 22. Near the end of the film when Ted's lawyer reads the court ruling, the ruling is dated Monday, January 23. If December 22 was a Friday (as it was in 1978), then it's impossible that January 23 fell on a Monday. In fact, the next time January 23 fell on a Monday wasn't until 1984.
During the court scenes, Ted's ex-boss Jim should had taken the stand and explained why he fired Ted as well answering other questions about Ted.
At 37 minutes into the movie Ted pours a dark brown drink from a bottle labelled J&B. J&B is famous as a pale whisky.
Ted after being fired gets another job just days before Christmas. In reality it would be impossible to get a job so near that time of year. In fact it wouldn't be until January or February he would be able to get a job after being let go.
Ted clearly wasted his time getting another job because getting another job with a lower wage income would work against him. Ted's lawyer should also be aware that Ted has lost his case because getting fired, coupled with a lower paid job will not win him the case.
The trees are green in scenes which supposedly take place in New York at Halloween and Christmas.
Early in the movie, when Billy's room is dark, a turned on lamp has a cloth over it. This could be extremely dangerous, especially in a child's room, where the heat from the bulb could set fire to the cloth. Later in the movie, the lamp is off, with the cloth hanging over the top.
When Kramer takes Billy to his office in NYC, he points out the Chrysler Building. Then they walk down the hall to his personal office, and he points out the UN Building. Therefore, they were walking north. Kramer then points north of the UN Building and says that way down that way is Brooklyn. He was pointing at the Bronx, while Brooklyn would be south.
When Ted has to let Joanna spend time with Billy on a Saturday, their meeting is set for the "Boat Pond" in Central Park per Ted's lawyer. They actually meet in the Esplanade. This is the same location where Ted watches Billy ride his bike earlier in the film.
Given the very close business and personal relationship Ted had with Jim, Ted's boss at his first job, it is unthinkable that Jim would fire him in the middle of a custody battle, not to mention, so close to Christmas, and without even a hint of suggesting child care, which was much more affordable in the 1970's. Ted could not possibly have been the only single parent at the firm.