They generally will not eat any left over dry patches.

How is the humidity in the tank?

A nice lukewarm dechlorinated water soak or spritz can help.

Prevention is best. They will shed nicely if they are well-hydrated. Concerns of dry skin or a dry shed:

Less oxygenation through skin due to tough, dry skin

Concerns for skin tears while trying to remove shed (never pull it off for them, just rehydrate)

Loss of electrolyte transfer

I'm guessing you might just need to boost tank humidity?