This morning I’ve rebuilt an old Special 20 of mine for a student.
A multitude of issues can be solved by simply disassembling, cleaning and screwing back together. Gunk on the reeds or in the tight gap between the side of the reed and the reed slot is common.
The method I use is to simply make a solution of white vinegar and bicarbonate of soda and gently (gently!) scrub all the parts with a kid’s soft toothbrush. Make sure to rinse thoroughly in running lukewarm water as the solution will cause tarnishing if left in contact for long. Pat dry with kitchen roll and it’s ready to screw back together.
Some harmonicas, like the venerable Hohner Marine Band, have a comb made of wood rather than plastic. Even if the wood has been sealed against moisture I’d be wary of getting them too wet and instead thoroughly dry-scrub with a stiffer brush.
Here’s a handy hint for keeping track of your reed plates.
The blow plate has the rivet end of the reed flush with edge of the reed plate. When mounted the rivet side should face downwards into the comb.
The draw plate has the free ends of the reeds flush with the edge. The reeds should be on mounted on the outside of the comb.
If you’re careful it’s difficult to do much damage with this method. Good luck!