The title "A Fox, a Rabbit, and a Cabbage" is an old riddle which FBI Agent Pepper (Keegan-Michael Key) asks FBI Agent Budge (Jordan Peele) in the FBI file room. The riddle involves a man in possession of a fox, a rabbit, and a cabbage, trying to get them all across the river in a boat. The man can only take one object at a time, and the fox will eat the rabbit if left alone, the rabbit doing the same with the cabbage. The answer is to take the rabbit so the fox will not eat the cabbage, go back and take the cabbage, taking the rabbit back so it will not eat the cabbage, then swapping it for the fox, then finally going back for the rabbit.
Burt (Stephen Root) calls "Mike" "Friend-o". This term is used by Anton Chigurh - directed at someone he might kill - in the movie No Country for Old Men (2007). Chigurh actually kills the character played by Stephen Root, who is playing Burt here, in that movie.
Lester (Martin Freeman) solves the riddle of the farmer who has a fox, a rabbit and a cabbage, and must get all three across the river, but can only carry two at a time. A nearly identical puzzle was solved by his character Tim Canterbury in The Office (2001) episode
Training (2001).
After Malvo treats his dental patient, he tells him "I'm still a little worried about the 203 and the 204." Human teeth are numbered between 1 and 32, while animals such as dogs have three-digit tooth numbers. This may have been an intentional mistake by the writers to confirm that Malva isn't really a dentist.
Lester has one heck of a commute from Bimidji, Minnesota, USA, because his office address is (approximately) 1119 10th Ave SE, Calgary, Alberta, Canada. A trip that will take a little more than 1000 miles and about 17 hours each way by car.