The "I Love Lucy" show was filmed in Hollywood several weeks in advance of the air date and never broadcast live as portrayed in the movie.
When the Castillo brothers first approach New York City in the early 1950s, the World Trade Center towers are visible in the skyline; they weren't built until the early 1970s.
The "Valentine" opening credits seen in syndication were *not* the original opening credits. When the series originally aired on CBS, the credits featured animated stick figures of Lucy and Desi along with the sponsor's product, such as Phillip Morris cigarettes. The "Valentine" credits were added when CBS began rerunning the series in 1958.
In 1952 the family watches an episode of the TV series Cheyenne (1955)--which did not premiere until 1955.