When using the new admin, you can create a discount code with the name of (for example) My_Discount-123_2015. All will seem to work fine; the discount is saved, no errors are generated. But if you try to use it, you'll get an "invalid discount" message in the cart.
After switching back to the Flash admin, I found the problem: you can't use anything other than letters and numbers. The Flash UI blocks these characters; the new admin does not, and saves discounts that do not work.
Non-ideal fix: Pop up an error message when a user saves a discount code with non-allowed characters, or prevent them from entering those characters in the first place.
Ideal fix: Let us use special characters in discount codes.