The DC-3 did have one Achilles Heel: It had miserable stall characteristics. If you ran out of airspeed, it had a nasty tip stall that would put you into a spin. It took about 3,000 feet to recover from a stall. There are two crashes that occurred in Montgomery County, MD in 1957, where the DC-3s stalled and spun in on training flights, one from Capital Airlines one from the Air Force.
I remember interviewing a former Capital Airlines pilot. He told me the DC-3 was a good airplane, but it would "turn around and bite you" if you got inattentive. Another story he told me was that many Capital pilots came straight out of the Air Force flying the latest tricycle gear fighter jets. They'd put these fighter jocks behind the controls of the DC-3, and the DC-3 would end up embarrassing them. These guys had a hard time handling a large tail dragger like the DC-3.
It's a stately and majestic aircraft, and the fact that so many are still airworthy 80 years later is a testament to their design.