It doesn't hurt to take a look under the kitchen sink for signs of trouble every once in awhile. Besides finding faucet leaks you may find that there is a problem with the garbage disposer that you weren't aware of. Discoloration can be a sign of corrosion on a garbage disposer. You may not notice anything wrong until there is a problem and you have to troubleshoot the garbage disposer because it stops working.
Try shining a light under the sink while running water and the disposer as you look for leaks. Look at the bottom of the faucet, at each pipe joint, at the sink strainer, and all around the garbage disposer. The repairs are usually easier if you catch the problem early.