Before the hot oil is poured into containers for any kind of storage, it should be poured through filters- Old T-shirts to remove any large debris, but those cotton coffee filters will work to remove blood, and small debris from the oil. The oil that comes out of the filter will be almost like water in color- a bit on the yellow side-- but decidedly pale.
YOU can't Filter Rendered FAT ENOUGH. When in doubt, add more filtering materials.
I use a spaghetti strainer, lined with cheese cloth, and/or old clean T-shirts. Then I put coffee filters- for my drip pot-- into the strainer on top of the shirts, or cheesecloth and pour the oil onto the filters. The strainer sits over a very large Bowl. When the oil in the bowl begins nearing the bottom of the strainer, I remove the strainer to another pot, or bowl, and then pour the filtered oil out into jars for storage. I repeat until I have filtered all the hot, rendered oil, and filled all my jars.
Let the oil cool to room temp, unless you want a partial vacuum in the jar to aid in avoiding spoilage. Without debris, or water in the oil, the oil will not go bad. Just keep it cool.
The Debris carries in the bacteria, and water gives bacteria a place to swim and multiply. The Debris often provides a food source for the bacteria. Its the waste from the bacteria that spoils the oil. You can refilter the oil to remove the waste, then heat it back up to kill any remaining bacteria, and then refilter the hot oil again for storage and use. The heat should make the oil suitable to use for cooking again.