In "Gridlocked", when Tilly squirts the mud off the car with the fire engine's nozzle, its license plate number is T8675309.
"Paint Misbehavin'" contains a pair of references to Homestar Runner: Tilly's version of coffee is skim milk and gummi bears, a reference to the Strong Bad Email, "bedtime story." Cricket later displays a painting based on Trogdor.
"Big Deal" has Cricket throwing a mallet to a giant TV screen, spoofing the famous Nineteen Eighty-Four Apple ad.
"Night Bill" has the Greens race against Bill's boss in office chairs, in a parody of the chariot race from Ben-Hur.
The final scene of "Cricket's Place" where it's revealed Cricket was telling the events to a woman at the park on a bench references the Framing Device of Forrest Gump.
The CGI video game sequences in "Level Up" are in the style of Minecraft.
When the family enters the library, Bill warns them the library is A Quiet Place and is full of rather strict librarians. The family spends the majority of the episodes struggling to not make even one sound — not even talking or whispering outside of sign language — otherwise the librarians will hear and throw them out.
Bill saying "I love you" in sign language and screaming to save Cricket from the librarians is a direct parody of the ending of A Quiet Place.