Taking a gun to a TV show

They probably never think to search guests on the show.

It would be very hard nowadays, but the setting of the film is more like the 80s. People were a lot more relaxed about security pre 9/11.

This takes place in 1981...different era for sure when it came to societal expectations and fears and the precautions they would take.

Like others say it was the 80s and pre 9/11

In 1981 in the real world he probably would have been if in some places like New York, as they were being cautious around celebrities for a bit after the shooting and killing of John Lennon on Dec 09th 1980 in case of copycats. However in a fiction like this real world events don't really play into it much, even then in those days not all parts of the US would have tightened security because of a high profile celeb killing like Lennon's.

Basically even then in that time Lennon's killer Mark David Chapman bought the gun in Hawaii and was able to bring it with him to New York without it being checked in or noticed on a flight.

To put that in some perspective, that was just coming out of the high terrorist era of the 70's, where for instance between 1970 and 1979 there were 112 domestic plane hijackings and terrorists had killed 184 people in the States and injured more than 600 others.

Here: https://edition.cnn.com/2015/07/28/opinions/bergen-1970s-terrorism/index.html

And yet Chapman was able to do that in 1980 because:

https://www.syracuse.com/celebrity-news/2015/12/john_lennon_mark_david_chapman_legal_gun_ny.html

Authorities at Honolulu's airport said Chapman probably got the gun past airport security simply by placing it in his luggage. At the time, baggage checked with an airline was not searched or X-rayed. Chapman flew first to Atlanta, then on to New York City.