The inside of the windshield has an oily film, and the A/C cooling is inadequate.
An oil film on the windshield could be cause by a refrigerant leak in the evaporator core that may allow some refrigerant oil to escape into the evaporator case. A/C blower motor operation in the defrost mode could carry the oil through the ducts to the windshield.
A plugged heater case drain would not cause an oily film on the windshield. An oily film could only be caused by a refrigerant leak or by a heater core leak. A plugged case drain could cause water to leak out onto the carpet or possible a musty smell coming from the vents.