How can I find the unique parts in the 71040 Disney Castle?
According to the review from Rebrickable these are the parts in new colors:

Aside from the Minifigs, there are no new part designs. There are plenty of parts appearing in new colors though.

Dark Blue 3943b - Cone 4 x 4 x 2
Dark Blue 44375a - Dish 6 x 6 Inverted
Dark Blue 3685 - Slope 75° 2 x 2 x 3 Double Convex
Dark Blue 98560 - Slope 75° 2 x 2 x 3 - Solid Studs
Dark Bluish Gray 99301 - Slope 33° 3 x 3 Double Concave
White 18838 - Brick Arch 1 x 12 x 3 Raised Arch with 5 Cross Supports
White 20310 - Brick Special 1 x 1 with Scroll with Open Stud
White 19121 - Fence Ornamented 1 x 4 x 2 with 4 Studs