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A recurring character trait of Randy's is his being prone to overreacting and obsessively seizing upon irrational ideas and fads, whether by himself or as part of a large contingent of the town's adult population. Randy frequently attempts to appear cool and popular, particularly to Stan, who finds his attempts embarrassing unless they benefit Stan's interests in some way.

Among the endeavors on which Randy sometimes embarks are get-rich quick schemes or other strategies for economic or material gain. In "Something Wall-Mart This Way Comes", he took a job as an associate at Wal-Mart. In "A Nightmare on Face Time", Randy buys the closed Blockbuster Video in town, hoping to turn it around. In "Black Friday", he takes a job as a security guard at the town's shopping mall during the Black Friday to infiltrate the mall before the stampede of shoppers. In later seasons, Randy is shown to have finally achieved a very high income from both his work as Lorde and his marijuana business, though this has not improved the underlying problems in his family relationships.

Randy has known his wife, Sharon, since childhood. Taking liberties with its floating timeline, the show establishes Randy and Sharon as being young adults during the flower power era. They maintain steady friendships with the parents of Stan's friends and are revealed as enjoying the act of watching pornography together to enhance their sexual relationship. However, their marriage has not been without its frequent arguments, which are usually instigated when Sharon is annoyed, ashamed, or disgusted by Randy's eccentricities. The two briefly divorced on two occasions, but quickly reconciled both times. Randy tends to showcase liberal viewpoints, having protested the 2003 invasion of Iraq and supported Barack Obama during the 2008 presidential race.

Randy dropped out of high school and was a member of a boyband in his teens, as shown in "Something You Can Do with Your Finger", but he has mentioned that he attended college and has been indicated to hold a doctorate. The show frequently depicts Randy to be a moderate to heavy drinker, and numerous episodes have dealt with Randy's belligerent and negligent behavior brought upon by his severe intoxication.

A few instances of personal achievement have made Randy a hero in the eyes of his friends and fellow townsfolk, such as being awarded a Nobel Prize and twice setting a record for producing the world's largest piece of human excrement. Randy has conversely been subjected to ridicule from the entire town, ranging from when he inadvertently accelerated the effects of global warming by suggesting the entire populace take on a more uninhibited approach to passing gas to avoid the hazard of spontaneous combustion to when he reluctantly exclaimed "niggers" while attempting to solve a puzzle during a live broadcast of Wheel of Fortune. In addition to the professional singing he did in his youth, Randy can also play guitar, as seen in "Guitar Queer-O". He can also speak a little Mongolian, having learned some in college, as seen in the episode "Child Abduction Is Not Funny".

The episode "Gluten Free Ebola" revealed that Randy produces music and performs as the noted musician Lorde, a fact that was explored subsequently in "The Cissy". This has become a running gag that has continued through multiple episodes, such as suggesting much of the Marsh family's income comes from his music career as Lorde rather than his geology job. As of season 22, Randy quit his job and moved the family to the countryside, where he sets up Tegridy Farms to grow and distribute cannabis. Throughout season 23, Randy engages in increasingly unethical business practices until he is sent to prison in "Season Finale"; though Randy is eventually released, he vows to no longer engage in illegal activities, though the cannabis season ends shortly after his release. In "Christmas Snow", Randy begins selling cocaine during the winter, which he has legalized in multiple states so that he can farm it. Finally, after years of the Tegridy storyline, Randy finally sold the farm and moved back to South Park in "Sickofancy".