The music heard when Niles and Frasier are riding their bikes is from the Overture to The Barber of Seville by Gioachino Rossini.
The title has a twist on the genetic term fraternal twins.
Frasier makes a common mistake when he says that the station will hold its first annual bike-a-thon. "Annual" means occurring once every year. Nothing is considered annual unless it's happened twice: until the second occurrence, it's merely a one-time event. Therefore, it would have been correct for him to have said that it was an "inaugural event," implying a formal beginning.