Barney's free agency speech almost exactly mirrors basketball superstar LeBron James' speech when he took his talents to South Beach to join the Miami Heat in 2010.
About 11 1/2 minutes in, Marshall's boss says "that man is the human equivalent of what came out of my body after eating that soup you recommended." This soup is from the restaurant that Lily got soup from just before she found out she was pregnant (The Blue Bowl Restaurant, in the episode "Challenge Accepted"). She said her and Marshall continue to eat there despite getting food poisoning there on at least 3 occasions because it is so good.
At the beginning of the episode, the first interview for the strip club "Moneyballs" is a reference to the movie Moneyball. "Moneyballs" uses sabermetrics, in the movie they use sabermetrics to put a successful baseball team on the field.
Around 15 seconds in, Barney says that he went to the Lusty Leopard for seven years.
This is another reference to LeBron James, who plays in Cleveland for seven seasons before he moves to Miami, since 2003/04 to 2009/10.
When Barney imitates Ted, he actually imitates "Ted" from "Bill and Ted's Excellent Adventure".