The other team's thief, "Apollo," is played by Apollo Robbins, a technical advisor for Leverage who taught Beth Riesgraf how to pick pockets for her role as Parker and consults in scripts. He is known as "The Gentleman Thief" and is regarded as the best pickpocket in the world, although he does so only for educational and entertainment purposes.
Christian Kane wore multiple hats for the duration of this episode to cover an injury he got over his eye while performing his own stunts in the previous episode. The cut he has that is seen later on (allegedly an injury the character received in a fight in this episode) is his real injury.
The backstory involving the recovered Klimt painting parallels the real story of the theft of another famous Klimt painting and the decades-long struggle to recover it for the family that owned it. Klimt's "Portrait of Adele Bloch-Bauer I" (also known as "The Lady in Gold") came into the possession of Klimt's brother; during the Nazi period he fled Germany for his safety, and the Nazis confiscated all his possessions illegally. His family attempted to reclaim the works after WWII, but the Austrian government opposed them on various technical grounds and held the paintings as state property. After a lengthy series of lawsuits and arbitration, most of the stolen paintings, including "Adele Bloch-Bauer I," were returned to Klimt's family in 2006. It was sold for a record amount to the heir of the Estee Lauder makeup company, who, in keeping with the family's wishes, donated it to the Neue Galerie (specializing in 20th Century Austrian art) in New York City, where it is now on permanent display. The whole saga was dramatized in Woman in Gold (2015) starring Helen Mirren. No elaborate con-artist break-ins were involved.
When describing the other team, Hardison says that the police call 'Chaos' Kobayashi Maru. This is another Star Trek reference. Kobayashi Maru is a test carried out at Starfleet Academy and refers to an unwinnable situation. Wil Wheaton, who plays Chaos, also played Wesley Crusher in Star Trek TNG.
If you are a good listener, you can find a little Easter egg. As the guards are watching the basketball game before the heist, listen to what the TV says. It says "and that's a steal by Parker..."