Finding missing items in an int list
For this

full_set = set(xrange(smallest_item, largest_item + 1))


I'd suggest inlining the min and max:

full_set = set(xrange(min(original), max(original) + 1))


You don't need to convert to a list before using sorted so:

sorted(list(full_set - original_set))


Can be written as:

sorted(full_set - original_set)