Nearly each episode features a family dinner. This was at Tom Selleck's request to keep a sense of family. He also states that this scene is usually one of the longest ones to shoot. The family dinner happens always each Sunday around 17:00 to 17:30.
Although they play father and son, Len Cariou is only five years and four months older than Tom Selleck.
The actors who play Jack and Sean (Danny's kids) are brothers in real life in which Jack is the older brother and Sean the younger.
In Shoot the Messenger (2014), at the Sunday's family dinner there is talk about the Theory of Broken Windows. The Theory is that minor offenses that are not addressed can lead to more serious crimes, making an analogy with a house whose windows are broken - if nothing is done, eventually the others windows would be broken too, and that could lead to more important crimes as throwing trash in it, breaking the furniture or burning the own house. It was written by George L. Kelling and James Q. Wilson and published on March 1, 1982 on the newspaper The Atlantic Monthly. Later it turned in a criminology book written by George L. Kelling and Catherine Coles and published in 1996.
In Justice Served (2013) you can see that Jamie carries a picture of his late brother Joe tucked inside his police hat. This also appears to be the same picture of Joe that's shown in the beginning of the show's pilot episode on Frank's bureau while Frank is getting ready to attend Jamie's graduation from the Police Academy. The actor shown in the photo is uncredited.