Chris, Its much better to remove all of the old shed. Like i said if there are small areas of stuck shed , just use a little mineral oil and it will fall off by itself. Always check to see that the eye caps are in the shed that just came off also.
I would like to add, That poor shedding is normally the result of no or low humidity. If you keep your snakes on paper you will have shedding problems if you don't add a little water to the cage every week. If you use aspen or cypress just add about a half a cup of water to the substrate every week. Hope this is helpful to you.
