Undersized (or overloaded). The longer the cord, the lower the load it can carry. Any cord used around the barn should be a hard service or junior hard service cord (typically round, not flat). And make sure it’s rated for the load.
Extension cords shouldn’t be used with water heaters, coffee makers, microwave ovens, or anything else that heats up. Their power demands are too high.
Use of gang plugs that lack overcurrent protection (those cheap outlet adapters that let you plug three things into one outlet).
Tightly coiling up cords when they’re in use. Tightly coiled cords can’t dissipate heat.
I do a lot of OSHA-type walkthroughs. The most common problems I see with extension cords:
– Damage to the outer insulation, often covered up with electrical tape, or damaged strain relief, where the cord starts separating from the plug, exposing the wires inside.
–Missing grounding prongs
–Extension cords substituting for permanent wiring (such as the ones used with fence chargers. If you have to leave it plugged in for the entire winter, think about installing an outlet).
–Daisy chains - one cord plugged into another, or plugged into power strips.
–Cords run over rafters, through windows, through doorways - where they can’t easily be checked for damage.
I haven’t heard of discoloration being a reason to replace a cord. But if you’re using it outside, make sure it is designed for outside use. And I would certainly want to make sure the insulation still feels flexible on a discolored cord.
I don’t know if any specific test to perform - other than using an outlet tester, one of the handiest gadgets I own.