Keep in mind that a steering damper has no effect only your steering whatsoever for the most part. You can take it off entirely, drive around for a week, and it really won't feel any different.
For this reason, it's quite amusing when you see people go out and waste their money on "performance" steering stabilizers, or even better, "dual steering stabilizers" (which are an even bigger joke), as if it's going to some how make their steering better.
Quite the contrary actually. What some of those very stiff dampers will do is fight your steering in one direction and cause your power steering pump (and your hands) to work harder to turn the wheel.
The only reason you'd ever need some insane setup like that would possibly be if you were doing Baja style dessert racing, where you were hitting washboard roads at high speeds. At that point, much like the steering damper on a performance sport bike (motorcycle), the steering damper would dampen the high-speed shimmying / side-to-side movement of the steering. It won't get rid of it entirely, but it will dampen it to some degree.
The moral of the story is that you can replace your steering damper, but if you do so, don't spend tons of money. Buy a Monroe damper, or something cheaper like a Rancho, OME, etc. Don't waste money on a part that isn't going to do anything for you.
A bad steering damper would have no symptoms whatsoever. I can also say with certainty that those little scratches and minor dents on it, are not enough to cause it to fail.