In the episode "The Carpool", Axl's knowledge of black holes is due to constantly watching Hot Tub Time Machine.
Dawson Casting: When the show started, Axl is a high school freshman and he's played by a 19 year old. Sue, a seventh grader, has an 18 year old actress. Brick is supposed to be in second grade, but the actor playing him is 11 years old. To be fair, the actor playing Brick (Atticus Shaffer) has Type IV Ostogenesis Imperfecta (also known as brittle bone disease), which causes him to be a lot smaller than average.
For the same reason, he is almost never filmed walking all by himself within a certain distance of the camera, as he has a noticeable limp.
A rare forgivable example in the cases of Axl and Sue since both actors actually do look much younger than their actual ages. Even at the age of 23, the actor who plays Axl still looks like a teenager. Though the same can't be said for the actors who play Darren and Sean who both look like they're in their late 20s. It was even lampshaded in the episode where Sue wanted to date Darren with Mike objecting because "he's 18 and he looks 30!"
Sue does strain credulity a bit early in the third season when she tells Frankie she just had her first period, given that Eden Sher is, uh, quite a developed young lady.
The Character Died With Her: Aunt Ginny. At the end of the third-season episode "The Map", which had begun with the Hecks coming back from her funeral, there was an In Memoriam to Frances Bay, the actress who had played her until her death several months earlier.
Reality Subtext: Plots in two episodes are based on events from the actors' real lives. Atticus Shaffer once went out for Halloween as the same obscure Scottish World War I hero Brick did in the first Halloween episode, and Patricia Heaton's family once hosted a Japanese exchange student who didn't say a word to them for two weeksójust like what happens in "Foreign Exchange".
Frankie's later retraining as a dental hygienist mirrors one of the show's creators, who formerly worked in that capacity herself.
Brick's actor has Osteogenesis Imperfecta, and was born in 1998.