Other mistake: How could Argie and Barker get round the skateboard track and up the stairs to the platform, especially with Barker, in less than 5 seconds?
Other mistake: At the party after award ceremony, we see the awards are dated 2012. Artie says he is 58, meaning he was born in 1954. He says Alice was born when he was 23, so in 1977, and she says Harper was born when she was 26. This would mean Harper was born in 2003, but she says she's 12, meaning it would really be 2015.
Continuity mistake: In the subway toilets, Argie checks two cubicles and looks in the third one. However, in the next shot, he is looking in the fourth cubicle.
Continuity mistake: In the scene where Billy Crystal is chasing his grandson at the recital, he has day-glow paint on his face. A few seconds later in front of the stage, the day-glow paint is gone.
Answer: It's demonstrated throughout the film that Artie struggles with the modern way of doing things. This may extend to modern car seat belts with their five point harness systems. That and the fact they're already late for school and holding up the traffic makes it a stressful situation for Artie and it was probably easier (and to add comedy) for Artie just to rip the seat out with the boy still in it.
Neil Jones