Lavan,
No, nothing quite so dramatic as the gun exploding, or the barrel popping off...
The main problems are related to the cylinder, and cylinder lockup.
One of the first signs is that the cylinder timing is no longer as tight as it once was. That's because the hand, the little gizmo that pushes the cylinder around, and the notches that the hand pushes on, start to peen. Essentially, the notches become larger, and the hand becomes shorter. Essentially, the cylinder goes "out of time" in that just as the hammer starts to drop, the chamber is no longer perfectly aligned with the bore.
This is also intimately connected to cylinder lockup. The cylinder bolt, the little stud that pops up through the bottom of the frame just above the trigger, will also peen and wear, meaning that it no longer holds the cylinder as securely in place when the gun does lock up.
In truly serious cases, the cylinder can "free wheel" or spin without locking up at all.
The other problem point is known as "end shake." This can be tested by grabbing the cylinder with the action closed and trying to move it back and forth toward and away from the barrel. A little movement (like less than the thickness of a business card) is normal. Much over the thickness of a business card, and the gun is developing an endshake condition.
I've seen Smith revolvers that have such severe cases of endshake that it is iffy if the hammer will ignite the cartridge, or just shove the cylinder forward and slightly dimple the primer.
Both situations can be fixed.
If the hand is worn, it is replaced. If the notches are worn, the ejector star is replaced. Both some fine fitting to ensure that timing and lockup are correct.
Installing a new cylinder bolt isn't much trouble either, generally requiring even less fitting, just a little tweeking.
The endshake problem can be more complex, but can be fixed either with special washers that go on the cylinder yoke (available from Brownell's) or through stretching the cylinder axel. The stretching step requires more experience and more tools to do properly.
I've got a Model 19 that has pretty bad endshake. I got it well used, and I've contributed to the problem over the years. I'm going to tackle it this summer, by stretching the cylinder axel.
This never really became a problem with Model 19s until police forces started training regularly with their duty ammo. At one time, most training was done with light .38s, and the gun was rarely fired with full-bore .357s. Then training started to be done with the duty ammo, and the complaints started cropping up a few years after that.