Leslie Nielsen actually appeared in a few episodes of the TV series The Fugitive (1963), which, of course, inspired the Harrison Ford movie The Fugitive (1993), which this film parodies.
When Leslie Nielsen's character Ryan Harrison jumps away from the bus as it gets hit by a train, Ryan lands on a bicycle that doesn't have a seat. In The Naked Gun 2½: The Smell of Fear (1991), Frank Drebin tells Hapsburg that the truth hurts but not as much as jumping on a bicycle with no seat.
The detective that was given the blood sample at the original crime scene is addressed as Van Adder, a reference to the lead detective from the O.J. Simpson trial. Also, he's told not to walk around with it all day, a reference to the Simpson investigation in which a blood sample was left in a police vehicle all day and spoiled due to the heat.
In the hospital scene, the intercom pages "Dr. Benton, Dr. Carter, Dr. Greene, Dr. Weaver, and Dr. Ross", all doctors on the NBC drama ER (1994).
Shari Lewis: As the voice of Lamb Chop, who appeared during the concert at the beginning of the movie. It was Lewis' final on-screen appearance. Lewis died on the evening of August 2, 1998 due to viral pneumonia, just 19 days before the movie's theatrical release in the United States.