I have some olive oil that has gone a bit cloudy. What causes that to happen, and is it still safe to use?
The most likely reason is that it was stored too cold (= in the fridge). If this is the case, then it is perfectly safe to use.
Some oils are also sold unfiltered. They don't really "go" cloudy, but are that way from the onset. But it can happen that the sediment falls to the bottom over time, then somebody shakes the bottle and it looks cloudy again.
If you had filtered oil sitting on a shelf and it turned from clear to cloudy, then this is suspicious. It is unclear what is causing the cloudiness in this case, but it is probably not doing anything for the quality, and has some potential to do harm (although there aren't many pathogens which can survive in a bottle of pure oil). Throwing it out would be on the safe sid.