I've never had any trouble under normal circumstances. Guns aren't normally a problem around here unless there's something else going on that gets people's hackles up. Be sure to not OC in any licensed liquor establishment in New Mexico. This includes gas stations, Walmarts and any other place that sells any kind of alcohol. You can carry concealed in places that sell for off-premises consumption and some restaurants, but not openly or unlicensed.
Don't carry openly in the Mesilla Valley Mall, they say carry's off limits there, but they aren't properly posted. If they do bother you, that's considered verbal notification and you'd better leave or get charged with trespassing.