This one is kind of sticky. Most underwriting systems are automated and look at all of the compensating factors, such as loan to value, debt to income, and cash reserves to account for a credit score issue. If you are trying to finance/refinance a higher risk loan (high loan to value, no reserves, high debt to income) then your rate will probably be impacted. It really just depends on the issues on your credit. If you have a bankruptcy under 3 yrs old or a foreclosure under 4 yrs old, odds are having you on the loan will substantially worsen the interest rates you are able to get. I do have to say I am occasionally surprised at what the automated systems will accept.
On a positive note it would be great for your credit to have a positive mortgage history reported to it.