Jay teaches Mitchell how to fight by introducing him to Brazilian Jiu-Jitsu, claiming he learned it from the legendary Gracie family. In real life, Ed O'Neill has trained for many years in Brazilian Jiu-Jitsu under Rorion Gracie.
In this episode, Phil is seen racing down the stairs and doesn't slip or trip on his way down...or up.
Manny beats Jay in chess with a so called scholar's mate. It's a very common strategy that contains only four moves and is often made right at the beginning of the game.