A payment made after the due date is in arrears. Even if you have payments that have been made in arrears you may still qualify for a competitive mortgage.
There are lenders that have loan programs which allow payments in arrears. The interest rate will be higher for this flexibility.
Depending on which account is in arrears, the lender may overlook the past-due amount. If you're dealing with a subprime lender, and the arrearage doesn't affect the property's title, then some lenders will allow the arrearage. An example would be a credit card that's in arrears.