After Oliver speaks with Felicity in the hospital, he receives a call from Barry Allen who tells him he "just woke up" and needs advice. This ties in to a scene in Pilot (2014) where Barry runs to Starling City and meets with Arrow.
The tune Count Vertigo whistles is "In the Hall of the Mountain King", a piece composed by Edvard Grieg for the play Peer Gynt. The scene this particular piece belongs to happens in one of the titular character's hallucinations brought on by getting intoxicated, making this a fitting song for Count Vertigo, who deals in hallucinogenic drugs.
This version of Vertigo is similar to the drug used by the Ra's al Ghul in Batman Begins (2005). In that film, Bruce Wayne had to overcome his greatest fears with Ra's al Ghul's fear toxin.
A Ferris Air banner is above the ring in the boxing scene. Carol Ferris is the girlfriend of Hal Jordan. Hal Jordan was a test pilot for Ferris Air when he became the Green Lantern.
During the boxing scene, one of the fighters support teams is wearing Wildcat robes. Wildcat was a boxer turned superhero for DC beginning in the 1940s, becoming one of DC's first non-metahuman or alien heroes.