Taunting "mall cops" is not a good idea, unless you know exactly where the limits of their authority are, and stay well away from them. Chances are, however, they know the law better than you, and it's not what you think.
In New Mexico, private security is licensed by the State, just like doctors, lawyers and accountants. This disqualifies, for example, anyone with a criminal record. Private security may carry firearms (but then again, so can everyone else in New Mexico, as long as you strap it on your hip and keep it in plain view, and you are not in a bar or a courthouse).
Commissioned public police, as well as private security, can be sued for false arrest. The standard is the same in every case: whether the arresting officer had probable cause to believe that the person arrested had committed a crime. Citizen's arrests (including arrests by mall cops) are held to a slightly higher standard, requiring probable cause to believe that a felony has been committed (not merely a petty misdemeanor).
The difference between a misdemeanor and a felony can be subtle. This is where knowledge of your local law can make all the difference. Where I live, petty theft is not a felony, grand larceny is. The difference is the value of the items. The value necessary to make shoplifting a felony in New Mexico is surprisingly small: US$250. Attempting to make off with a nice jacket or pair of shoes could be a felony.
Similarly, simple assault is a petty misdemeanor, but aggravated assault is a felony. Simple assault can consist of merely "the use of insulting language toward another impugning his honor, delicacy or reputation", whereas aggravated assault requires using or brandishing a deadly weapon, or, oddly enough, "wearing a mask, hood, robe or other covering upon the face, head or body" (since a criminal intent to inspire fear of injury is also required, insulting people while clothed is probably not aggravated assault, though the statute taken literally does suggest that.) Thus, if you go to a mall in Albuquerque and insult the mall cops while wearing gang colors, they can and will arrest you and deliver you to the City police or County sheriff.
Forewarned is forearmed.
Disclaimer: IANYL: (I am not your