It's not uncommon to see an AM station operating off-frequency. Get an SDR or load a public KiwiSDR, zoom all the way in on the waterfall spectrum and jump around the dial. You'll see many who aren't right on center, and many who are even beyond the ±20Hz FCC limit. Especially on the crowded "Graveyard channels". Stations running greater than ±100Hz off-frequency are seen a number of times per year. Those offset carriers become easy targets for DXers. Usually, those get fixed in the matter of days to a week or so. Sometimes it's the backup transmitter that is off-frequency, so a reported carrier offset may disappear for months or longer, then suddenly reappear for a night or two. 1130 KTLK's (Minneapolis, MN) backup transmitter has an offset of about -77Hz, been that way for years.
There's a list of these offsets that you can search, with dates showing when they were last measured.
1260 WNDE (Indianapolis, IN) has been running with an offset of +35Hz for number of years now. They cause a serious low rumble here at night, and they are often strong enough that you'll hear garbled distorted audio, either from WNDE, or from a weaker on-frequency station.
1070 used to be almost unusable here at night. 1070 KFTI (Wichita, KS) was at -24Hz and 1070 KSKK (Verndale, MN) was +62Hz. Those made hearing KNX out of Los Angeles especially tough. Fortuantely, KSKK appears to have fixed their transmitter within the past several months. KFTI has been off the air due to damage to their tower site by theifs.
Local listeners close enough to the off-frequency station really wouldn't notice. Manually tuned radios can easilly be bumped to the right position, and the PLL in digitally tuned radios shouldn't have a problem locking to a carrier that is a few hundred Hz off. It's when night falls and other stations who are closer to being on-freqency start to come in. Those will cause low rumbles and distortion, especially for listeners who are on the outer parts of the listening area.