The heat in my 74 roadrunner is still blowing down on the floor and defrost vents even when the levers are in the off, low temp position, and the blower is off. I've looked all over the box and can't find a disconnected lever or one that isn't adjusted right or in the wrong position. The car is black/black and having the heat on is not fun.

make sure that the water valve is shutting off. If it isn't there is hot coolant circulating through the heater core.

Is this an A/C car? It sounds like one of the vacuum actuators is not working leaving the door open.

Slotts

I have no vacuum actuators under the dash and it is a non A/C car.

I would have to say that one of the doors has broken off inside of the heater box

No doors are broken off inside the box. and unless their is a water valve inside the heater core I don't have one. This car has 20000 original miles and still has the original 1974 heater hoses so nothing is missing.

On a non-A/C car there is no heater control valve.
Hot water is always running through the heater core.

A cable operated door is what blocks the hot air from coming through the vents. It might have a cable out of adjustment, or has come loose at the control panel or heater box.

Some people install a manual heater control valve in a hose to block the hot water from ever going to the heater core.

I know in earlier cars there are little foam seals that rot away, so even when the door is closed, you still get air flow since the seal is gone.

Thats the thing. I've replaced seals and put new foam in the box all doors are working and intact. but when I drive enough air moves through the box from the cowl to blow into the cabin and make it extremely uncomfortable in 90* weather. Today I made two special plugs that go into the inlet and outlet that block the water and still allow me to have the heater hoses in place. After I did that I let the car warm up and went for a ride and it was fine.

My cuda is the same way.. always some hot air coming out.