The Jumanji game board was very popular throughout the years, to the point where a screen used board was sold in 2014 for $60,800. 

The gun shop owner asks Van Pelt if he's a postal worker. Around the time of the movie, there had been a lot of news stories about postal workers going crazy and shooting up their workplaces, from which we get the expression "Going Postal." 

When Van Pelt enters the gun store, the music playing on the radio is the national anthem for Mexico.

When the film was released in Mexico itself it was changed to feature another musical score. It is an infringement of Mexican law to play the anthem for commercial or mockery situations, deliberately or not, although in the U.S. Territories it is in the public domain. 