A musty smell coming from a sink would likely be caused by hair and debris caught in the drain, the drain overflow or the drain trap. Clearing these are nasty, relatively inexpensive plumbing jobs and if you are not particularly handy you might want to let a plumber do them for you. If not, carefully remove the stopper from your sink by loosening the small bolt through the retaining clip on the stopper control rod (under the sink) and loosening the knurled nut around the ball joint that secures the stopper base to the control rod. Look down in the drain and you will see a rod about 6" down. Often hair and other debris get hung up on the rod and make a stinky sludge. Remove it with something like a bent coat hanger wire or bottle brush. If you are not on a septic system you are going to need something pretty strong like a bleach solution or commercial drain cleaner to clear the gunk out completely. (If you are on a septic system, check with your septic tank company to determine a safe solution to clear the drain and trap.) Now pour your strong solution down the drain and leave it overnight. Do not use the drain in the morning until you have flushed it out thoroughly with boiling water. Usually, an overflow hole is cast into a bathroom sink near the rim. If the sink is overfilled, water drains through the overflow hole(s), through a small passageway, and into the trap. Smelly, sludge-like material can build up in the inner chamber; causing odor .You can clean away this sludge with a strong solution of detergent and very hot water. Pour it down the overflow. If the smell persists, try a mixture of laundry bleach and water followed by thorough rinsing with water. If you can see sludge, loosen it with a stiff brush and rinse it away. If you think the problem is the trap and you just have to clean it yourself then, turn the water connections off, get a bucket small enough to fit under the trap and some towels. Normally there are large pipe nuts and seals on either end of the trap. If you loosen the bottom one first and push the securing nut and seals up the drain pipe (here's where the bucket comes in because the water in trap will spill at this point) you should be able to rotate and loosen the top trap connection (remember to keep the hex nuts and seals above and below the trap joints). Clean out the sludge and mess in the trap and reconnect it to the drain pipes.
Musty garbage disposal
If your garbage disposal will not freshen up with the normal vinegar, cleaner, or baking soda treatment, the rubber cover or splash guards may be dirty. Food bits and other debris can collect under the rubber flaps. This gunk stays damp and creates a strong smell. You may be able to get rid of it by suing a stiff brush or rag to clean underneath the rubber flaps. Running ice cubes through the disposal occasionally helps keep the flaps and impeller blades clean.
To test a shower pan, block off the drain, fill the shower floor with an inch or so of water and let it set to see if you see a leak. If so, where does it appear to be coming from? Most shower leaks do not come from a leak in the pan or the drain line. Most shower leaks come from the shower stream hitting the tile wall corner, floor and tub-top junctions where the grout has shrunk or cracked. This allows water to penetrate behind and dampen wood structural members or wallboard or allows the water to run down behind the lip of the shower pan and out on the floor, thus causing smells. Seal the grout and/or the wall/tub/floor junctions.
Sewer smell in home
If you detect a sewer smell in your house, there may be a dry trap in the drainage system. In homes with a basement, the smell often comes from a floor drain there. All drains to a sewer system have a shaped trap which is usually filled with water. The trap provides a seal to keep out sewer gas. If your basement floor drain is rarely used, the water may evaporate from the trap over time. Eventually the water level is so low that the seal is eliminated, allowing sewer gas (and smell) into your house. The solution is easy: pour water into the drain.
If this doesn't solve the problem, there may be a small leak in one of the vent lines of the plumbing system, or a small leak around the base of a toilet or other fixture. You may need the help of a plumber. Check for loose fittings, corrosion, or holes in vent piping. Also, check the top side of horizontal drain pipes. If the top is rusted, it may never leak liquid, but it will leak sewer gas. Drain lines made of copper, steel or cast iron may all exhibit this problem.