Factual error: When Julia Roberts and her roommate are in their living room and "I Love Lucy" comes on the TV, the opening theme song is accompanied by the traditional heart with "I Love Lucy" written on it. However, this movie takes place in 1953-1954, and that opening for the show wasn't used until the show was put in syndication many years later. During the show's primary run, cartoon characters of Lucy and Ricky opened the show.
Factual error: In the scene with the big band, the band is playing a tune in which the trumpets play the melody with a muted sound (this is kind of a "metallic" sound) yet the trumpeters don't have any mutes in their horns. They would have to be awfully good players to be able to make their trumpets sound like they are using metal mutes if there were none available. This is basically an impossibility.