I purchased a gallon of amazing Greek olive oil a few months ago. It has some floaty wisps in it now. Is it still safe?
From your descriptions it seems just freezing of some of the oil components.
When the oil is kept at low enough T, it is naturally subjected to partial of even full freezing.
White wisps, flakes and even little solid spherical drops can be seen, which tend to deposit at the bottom but are about floating in the volume if the recipient is moved.
This is totally normal, right as water inevitably becomes ice when the temperature is about 0 °C.
In the olive oil case, a denser liquid forms starting at about 12/10 Celsius and becomes evident as described above when the T is about 5 or 6 °C.
This is a normal occurrence during winter time whenever the oil is transported and/or stored in caves, supermarket corners, and even at home like in storeroom or balconies.
The oil slowly recovers its liquid clear appearance if left at normal room temperature and most important it is still safe and its organoleptic characteristics are basically unchanged, too.
There are tests based on freezing behaviour as for oils will have specific T profiles depending on their composition and possible treatments (e.g. filtration, ..) they could have been submitted to.
At a very deep level of discussion, an oil that underwent freezing might be susceptible of a faster rancidification, as for in the while the crystallized fat part is unprotected by natural radical scavengers such as phenols compounds naturally present. But this should matter to those dealing with the storage of trade/business amount of oil.
Recommended storage conditions are in dark and at temperature in the range 13 to 18 °C.
Here is a picture of a quite severe freezing:
Enjoy your oil.