Jerry O'Connell was on the varsity fencing team at NYU, which is why he looks so convincing in the scene where Quinn Mallory uses a saber to defend Rembrandt and his double in a world where America is a monarchy and Rembrandt is part of the royal family.
When Rembrandt is laying in bed talking to his double he places his hand on his stomach. At this point you can actually hear a hollow sound as if it were a ball or air filled cavity under his nightshirt.
The broadcast announcing the death of the King and his two sons is almost word for word the same as Walter Kronkite's announcement of the death of John F. Kennedy.
The pond that the gang talk next too is the same as Batman and Robin and X-Men