Mold could happen if moisture was introduced into the jar, possibly by dipping out with moist hands. I separate out a small portion - about pill bottle size, or a small squeeze bottle if liquid, to handle.

Added: I suspect that the more unrefined coconut oils (that have some solids separating at the bottom) would be more subject to the growth of mold, but not sure. Those are certainly the tastier oils. Its the introduction of moisture and spores that would be critical. In addition to hands, it could be introduced by moist spoons, leaving container open or other means.

Most coconut oil melts at 76 degrees F, but coconut oils can have different melting points depending (I think) on extraction methods. The other possibility is that the rooms could be slightly different temperatures.

Added #2 "In humid countries, the sun-drying of oilseeds with a high moisture content, such as mature coconut, is slow and inefficient (e.g., copra). Such conditions promote mold growth, which could result in high free fatty acid levels and poor quality oils." http://www.nowfoods.com/M013397.htm So it could also be a problem with the oil quality if you don't believe there has been any contamination at your end.