Conflict between wiggle expression [wiggle(5,5)] and auto-orient

Another thing that might help is if you use the Ease function on the Wiggle? I haven't had a chance to try it but thought it might ease the interpolation to smooth it out a bit? Rick? Mylennium? Any thoughts on this?

Other than what Rick already suggested, of course this could easily be fixed by smartening up the expressions to include the auto-orient function and an animatable wiggle amplitude slider...

Mylenium

Split the layer where the wiggle starts. 

Try parenting the animated shape layers to a null and apply wiggle to the null.

The workflow that will work the best depends entirely on your comp. If you have 10 shape layers and you want them to all wiggle independently as they approach the end of their motion path then you will need a null for each layer. If they can all wiggle the same way, then just one null with an animated wiggle will do the trick.