When Arthur, Francine, and D.W. go to see a movie called "Quazy Kool Kittens: The Journey Home", they can be heard talking out loud, up until they later decide to leave together. In reality, talking out loud in theater rooms is considered a public disturbance that can constitute being escorted out by theater personnel and facing legal consequences, including being banned from the premises.
In the intro to "D.W.'s Very Bad Mood" where Arthur's imagination is of a "Leave It to Beaver"-style setting set in about the 1950s, the character of Arthur refers to his parents as "Mother" and "Father". However, the words "Mom" and "Dad" have come into use even back in the 1950s, and the characters in said TV series Beaver Cleaver and his brother Wally Cleaver actually referred to their parents as "Mom" and "Dad".
When Arthur brings up the event to his friends where his sister D.W. was repetitively slamming the door to the bedroom she and Baby Kate both share, the issue of awakening and scaring her baby sister is not brought up, which would have actually happened, considering the fact that loud noises can wake up babies and cause them to cry.