One of the early ones is the crash of a BFW M.20 on the Berlin-Goerlitz route on April 14, 1931. In a gust the rear fuselage was twisted by 60°, the tail surfaces almost broke off and the aircraft crashed. The crash investigation concluded that the design was good enough to satisfy the certification requirements, but that flight loads exceeded those. As a consequence, the certification loads were doubled.
Also, the rudder hard-over with the early Boeing 737s comes to mind. Those accidents caught the poor pilots in a trap. And maybe the first deep stall with the One-Eleven in 1963. Later accidents with the Hansa Jet and the Trident could had been avoided had the engineers and test pilots studied the One-Eleven accident better. Tupolev did and increased the tail size of their Tu-124A (which became the Tu-134) by 30% as a reaction.
The 1991 Lauda Air Boeing 767 uncommanded thrust reverser deployment might also fit. It happened before, in 1990, on the C-5A when the thrust reverser of the No. 1 engine deployed right after takeoff. Similar to Hawker-Siddeley before them, Boeing refused to learn that lesson and tried to cover up this design flaw.
Borderline case: The Kegworth air disaster, when a fan blade on the uprated CFM56 engine of a Boeing 737-400 broke and the different sourcing of flight deck air caused the pilots to shut down the good engine. It turned out that the engines had not been sufficiently tested and the pilots had insufficient familiarity with the engine instruments, so they came to their wrong conclusions (which would had been correct on the earlier 737s).