Cloudy water (that clears after some time in the glass) coming out of a faucet means there is too much air in the water. Sputtering at the faucet is another sign of too much air in water supply lines. You have nothing to worry about if the problem clears by itself after running the water for about a minute. However, you may have a plumbing problem if it persists. Here are some of the reasons you may have air coming out of your water faucets:
Overheated Hot Water Heating System
If the sputtering is coming out of hot water faucets, then you have an emergency at hand. It may be that what you see as air is actually superheated water or steam. This usually occurs if the hot water heating system is overheated, a situation that can lead to an explosion or scalding incident. Turn off the source of heat for the water heater (electricity or fuel) and call an emergency plumber.
Water Treatment Equipment Malfunction
Air may also get into your water supply lines due to a malfunction of the water treatment equipment. Treatment systems meant to remove gasses (and hence eliminate odors) from water sometimes use air injectors, but they normally work in such a way that only water, and not air, flows through the outlet pipes.
However, a change in the settings can easily introduce air into your system. A good example is if there is a change in water output without a corresponding adjustment in the air injection rate. A clogging of the air release valve may also cause the same problem. Thus, if you have such a system, it's worth calling the water treatment company for a fix.
Damage in the Plumbing System
Anything that lets air into the water system can cause sputtering at the outlets. Therefore, damage to the water pipes may also cause this problem. If the air sputters are occurring at multiple faucets, then you are probably dealing with damage to the main lines, and your water utility company should know about it. If it's just one or two faucets, then call your plumber to diagnose and sort out the issue.
If you can't figure out the problem, then call a plumber for a professional diagnosis. As with all plumbing issues, delaying with the solution isn't advisable; if you don't know the cause of the problem, then how can you be sure it's not something dangerous?