Leaking water inside.

When it used to sit outside even while raining, I noticed that the carpet would get a bit wet. It looks like it's coming behind the dash and from the AC/heater vent(out front by windshield). Is this common on some cars? I'm hoping it's a stuck upon vent door rather than a rusted hole. Obviously I plan on checking it out soon, it's in storage. It's a 1971 duster :)