When Harry and Lloyd are in the car, Lloyd asks if Harry wants to hear the most annoying sound in the world. This was not originally in the script (you can tell by the look on Jeff Daniels' face).
After scamming Seabass to pay for their bill, Lloyd says he saw it on a movie. The movie he is speaking of is Something Wild (1986) and the guy who pulls the scam is played by Jeff Daniels.
According to the Farrelly brothers, Jeff Daniels wasn't wanted for the film, but Jim Carrey wanted him in it. In order to ensure a no from him, they offered Daniels $50,000 for the role. He accepted without any hesitation nor did he attempt to negotiate, despite insistence from his agent the film would "kill his career." By 1994, the film was Daniels' most successful.
In the bar scene in Aspen, the line "No way... that's great. We've landed on the moon!" was not in the script but made up by Jim Carrey on the spot during shooting.
Jim Carrey chipped his tooth years earlier, but had the cap removed for the film to make his character look more deranged.