The best thing I've seen (didn't get a chance to implement at our own facility because our nuts are all leaving in one month, but one of our suppliers does this) is using color coded dots (size of maybe a silver dollar or something easily visible) for each allergen.
For example, lets say blue is coconut, red is peanut, green is pecan and gray is walnut, you would then use these color dots on your pallet tag when you receive them in. If one has multiple allergens, then you use multiple dots.
You can easily see in this way if you are storing them incorrectly. You can have a pallet with a green dot and blue dot above a pallet with a green dot and blue dot and red dot, or just a blue dot above a pallet with blue dot and green dot etc.
You will also immediately see if you are storing green and red above green, and know that is not correct, or green and blue above green and gray.
Without color coding it can be difficult to tell if you have the correct order by simply reading tags and remembering what types of nuts are where.
Hope this helps! I really liked it and was sad I didn't have a chance to implement it.