The short answer is, yes they do. They are prone to become discolored with water spots, particularly if you live in an area where you are served by hard water. Hard water can leave a white stain on the faucets due to a build up in the minerals in the water. This build up is often hard to remove by simply wiping.
Taking a solution such as a citrus cleaner or rubbing alcohol diluted in water should remove this scummy residue quickly and easily if you rub it with a cotton ball.
Some people advocate the use of diluted vinegar and water and trying to softly scrub the faucet with an old toothbrush. It would have to be gentle enough so that it doesn’t damage the nickel finish.
Try to make it a habit of checking your brushed nickel faucets as well as the shower heads and knobs. If the water you use is hard enough to create noticeable marks on the hardware it will only get worse if left to harden over time.
Although the claim is that smudges and fingerprints will not affect your brushed nickel faucets, this is not 100% true. They will show up over time but they can be easily removed and measures can be taken to make it more difficult to reoccur.
If you find that there are fingerprints on your brushed nickel faucets you can simply prepare a weak ammonia solution and then wipe down the faucets using a soft cloth. To discourage the fingerprint marks from returning it is possible to use a neutral-color wax on the surfaces.