At around 26 minutes, Taylor yells out "LEE-ROY JENKINS!". This is a reference to an infamous online gaming incident where one gamer is shown heading recklessly into danger while the rest of his group is surprised that the previously planned approach was abandoned, thus leading to the decimation of the entire group.
Bill Hader and Dale Pavinski trained with a firearms instructor in preparation for the stash house shoot out scene. Hader had particular difficulty learning to reload his rifle without looking down. At one point he managed to reload the rifle perfectly. He was so pleasantly surprised that he almost ruined the take.
The case of "Box-Phones" that Fuches and Barry use for setting up alibis is shown to hold at least ten separate phones.
In the children's gym, the flag of the Soviet Union (which hasn't existed since 1991) is seen hanging from the rafters. The current flag of Russia is also present nearby. This is presumably a nod to the two Russian characters in the scene.
With 0.643 million viewers, this was the most watched episode of the first season.