There aren't many discounts in the mortgage industry (at least not "free discounts" as you might think of them). It is actually possible to purchase discount points to decrease your mortgage rate. Essentially, you are able to pay more initially to decrease your rate — and monthly total — by purchasing mortgage points, or discount points.
However, there are some rare cases where you can get discounts on other parts of the mortgage process. For example, NBKC Bank, the best mortgage lender for discounts, will give any Costco member a discount on their origination fee.
Of course, the biggest expense with mortgages will come in the form of your rate and subsequent payments, but every little bit helps.