If the shaking off animation gets interrupted by going out into more rain or coming out of the water into rain, the dog will stutter at whatever "phase" the animation was at when it went into the rain. Having the dog sit does not fix it. The only way to fix it is to let the animation continue by letting it dry off. I don't know if it affects wolves as the only ones I saw despawned before I decided to make a bug report.

Steps to reproduce
1. Find a wolf
2. Tame it
3. Wait till it rains
4. Quickly find a block without rain such as leaves or the overhang of a roof
5. While it is shaking, quickly run back out into the rain
If done correctly, it will stutter endlessly until it finishes the animation.