Vincent's car alternates between a 1983 model Chrysler LeBaron Town & Country convertible and a 1984 model. The front ends are the same, but the taillights are different between the two model years.
When Vincent and Oliver are driving back from the track with ice cream cones, Vincent's cone changes several times.
When Oliver is walking home from school on his first day in his gym clothes after his uniform is stolen, his shoes change from being white tennis shoes in one shot to grayish white basketball shoes in another.
When the bullies harass Oliver by the pay phone the blood spatter on Oliver's nose changes significantly from when he is against the wall vs against the ground.
When Vin and Oliver are riding in Vin's car after Oliver got beat up by the bullies by the payphone, one shot shows a low evening sun glowing behind them. However, the rest of the scenes from that same day show bright, overhead, afternoon sunlight.
When Oliver is gathering the facts about Vincent in Viet Nam from those who knew him, he is told that Vincent was a "Sergeant Major". Then, he's told about Vincent saving the guys in his unit and being awarded a bronze star. However, when they show the picture of him getting his Star from President Lyndon B. Johnson, there are 2nd lieutenant bars on his collar. Also, born in 1946 and going into the army at 18, would make Vincent a maximum 23 yo when Johnson left office. No one can make Sergeant major in 5 years, not even in a war; though he could have gotten a field commission to 2nd lieutenant.
During Oliver's presentation, he says that Vincent fought in the Ia Drang valley campaign as part of the 5th regiment and without specifying a division. On the US side, the battle was actually fought by 1st Battalion, 7th Cavalry Regiment of the 1st Cavalry Division.
Vincent is identified as having served in Vietnam while in the US Army. However in several scenes, Vincent is wearing an undershirt and clearly displays a USMC Bulldog tattoo on his left arm.
The film is set in the middle of the school year in New York, yet it is obviously summer.
The water at the nursing home doesn't move.
When the students are doing chin ups in gym class, the student before Oliver, only shown from the chest up, has limp arms and hands when he is doing his chin ups instead of tightened arm/hand muscles, which would be the case if he was really doing chin ups.
When the priest is introducing Oliver and tells the class the Oliver is Jewish, a few children speak up about their religious beliefs. One says she is also Jewish, one says she's a Buddhist, and another says 'There is no God'. The priest refers to her as an agnostic. An agnostic believes that no one can know if there is a God or not. The proper term is atheist, that believes God does not exist.
The receptionist in the hospital takes Vincent's cash for Daka's ultrasound copay without giving him a receipt.
When Oliver makes his speech, he mentions that Vincent fought at the Battle of Ia Drang. However, Oliver pronounces it as "La Drang" when the correct pronunciation is closer to "Ya Drang".