The mansion owned by Boris is actually the second largest private home ever built in the U.S., after Biltmore in Asheville, NC. Oheka Castle was built from 1914-1919 for Otto Hermann Kahn, who took the first letters from each of his names to give the mansion estate its name.
Reshma Shetty (Divya) is married to fellow actor Deep Katdare, and the last name of Divya's character on the show is Katdare. Deep Katdare also executive produced and acted in a movie, Hiding Divya (2006), which premiered three years before the premiere of Royal Pains (2009). Thus, both the first and last names of Resma Shetty's character on the show, Divya Katdare, are either a reference, or a tribute, to Shetty's real life husband.
The character of Paige Collins is an artist, and is portrayed by Brooke D'Orsay. Musée d'Orsay, located in Paris, France, is second in importance only to Musée du Louvre as a French art museum, and holds the world's largest collection of impressionist and post-impressionist masterpieces. Paige Collin's artist avocation is a reference to the actress sharing a last name with the important Paris museum.
Boris' magnificent home (Oheka Castle, one of the biggest US mansions, circa 1919), is actually west of The Hamptons and about 20 minutes from the North Port power station, whose four smokestacks can be seen in some shots. This means it would be unlikely Hank and Evan would see water from their patio, even though a jetty and water are always in the background, implying an ocean view.
The trivia items below may give away important plot points.
The pair of sunglasses Hank puts on at the end of the Pilot was saved by actor Mark Feuerstein. When seeing that the close of the series was a shot of Hank putting on the glasses, he brought them to the set. As a result, Hank closes the show with the same sunglasses used in the first episode.
During Dimitri's first two appearances he needs a translator because his English isn't very good. After his appearance when Boris and Hank rescue him from the Middle East and every subsequent appearance his English is suddenly good enough that he no longer needs a translator.