The big advantages of shoot .38 Special in a .357 Magnum is price, comfort, and wear on the gun.
.38 ammo is cheaper than the .357 and you can shoot more for less.
Since there is much less recoil and muzzle blast, the .38 is more pleasant to shoot.
.38 Special, being a less powerful round is much easier on a gun. In the case of guns like the S&W "K" frame, extensive shooting with full-power Magnums can cause accelerated wear on the gun requiring repairs.
Shooting standard load .38 Special ammo in a Magnum gun will cause the gun to last just about forever.
The only real "problem" with shooting .38 in a Magnum is possible chamber fouling causing chambering problems when you attempt to load a longer Magnum round.
The "Fix" for this is to simply buy a bronze chamber cleaning brush from Brownell's.
Unlike using over-caliber bore brushes, these chamber brushes are made of a special extra-stiff bronze bristle.
To use, simply push AND "screw" the brush through the chamber. Usually, one pass is all that's needed to remove ALL fouling except for really bad leading.
This is better than other methods, since there's no risk of damaging the chambers, and the chamber brushes work FAST.
One word of warning: I DON'T recommend using the stainless steel chamber brushes.
These, along with stainless bore brushes are for gunsmith use in guns so badly neglected, you have nothing to loose.
They can and WILL damage the bore and chambers.
There WAS a real problem with shooting short rounds in revolvers, but this was a problem of the 1920's and 30's.
In those days, ammo was corrosive, and there were many now obsolete short cartridges that could be fired in a .38 Special revolver.
What would happen was, the corrosive ammo would cause the chamber to corrode causing both a build up of fouling AND a ring in the chamber.
When longer ammo was fired, the case would swell into the ring and fouling and cause stuck cases.
This CAN happen today, mostly in carbon steel revolvers.
If shorter ammo is fired in a blue steel revolver, and NOT cleaned out properly, moisture can allow the steel to rust UNDER the build up.
When the gun is finally cleaned, you find a corroded ring in the chamber, and if it's bad enough, you can have extraction problems.
The answer: A Brownell's chamber brush and a good cleaning EVERY time you shoot your revolver.