They would never admit that.

Chevrolet "Series M Copper Cooled" (air cooled). This 1923 model was intended to compete with the Franklin. Unfortunately it was so awful, dangerously overheating to point of being hazardous to driver and passengers, that all were recalled and destroyed by Chevrolet except for two that survived and currently reside in museums.

The Chevy Vega from the 70s could possibly fit in that category. GM's engineering team was brilliant enough to run steel piston rings inside an aluminum engine block without steel sleeves and those cars burned oil like no tomorrow. Steel is much harder than aluminum and the rings slowly wore out the bores of the cylinders.

The Ford Pinto had the infamous gas tank disasters in the 70s as well. I'm not sure if that would go as a "quality" as in things breaking before they should, but it was certainly a failure of common sense to put a gas tank between a bumper and the live axle rear end with no crush space. 

I'm sure there are others, but those are the two glaring American examples I can think of off the top of my head.

That's a tough one, as most discontinued models - and manufacturers who were essentially sold for land and buildings, there are MANY problems besides terrible quality. They might have major design flaws, or crap materials, or they're ugly.

But if you want a nominee, I'll say the Sterling - it was supposed to mate a reliable Japanese engine (Honda V6) with British coach building skills. But the quality (especially the electrics) was so abysmal that what would seem to be an excellent design (Accords of that era were excellent) failed miserably.

Let me pose another question for the forum: what will be the next one?