I would not reuse that oil. The frying-oil reuse that occurs in fast food chains is reuse for the same day or over just a few days. They also store it properly and not just sitting exposed in the fryer.
justkt is correct that more saturated fats are less sensitive to breakdown, this is why bacon grease can be kept for a rather long time.
Three factors play a significant role in oil degradation:
Oxidation
Any contact with air causes oxidation in oil. High temperatures, metal alloys, surface exposure, and even UV light act as catalysts to this reaction.
Hydrolysis
When water interacts with oil it causes it to taste tainted or acidic. This is exacerbated by high temperatures, heating/cooling cycles, and oxidation products.
Polymerizaton
When frying oil deteriorates, the resulting products form both volatile (or reactive) and non-volatile compounds. Non-volatile compounds remain within the frying oil, and can produce polymerization at frying oil temperatures above 200°C (390 F) or in isolated hot spots within the frying system. These molecules bond together to form large, different-sized clusters that accumulate on the oil’s surface. Since they don’t dissolve, they cause foaming; trapping air under the oil, and increase the possibility of hydrolysis.
Given all these, the best environment for any oil is an cold, dark, airtight place. Cold temperatures may cause clouding, but this is not a cause for worry.
Source:
http://www.heatandcontrol.com/technical%20articles/Maximizing%20Cooking%20Oil%20Life.pdf
Best Answer
Fries cooked in animal fat will taste distinctly different than those fried in a neutral vegetable oil. They will be much richer in flavor and may make you weep with joy.
If you haven't had them, you must stop what you're doing and make some duck fat fries.
Here is a good recipe: http://hecooksshecooks.net/2009/03/duck-fat-french-fries/