Simple: what is worst (in terms of loss of life, or economic consequences) possible naval accident that could take place during the Cold War? Would it be possible for such an accident to have political consequences, beyond the sacking of an admiral, or a defense minister? More plausible examples/close calls that were averted are preferred.
For example:
Disaster: In early 1981, during a training exercise in the Arctic Ocean, Typhoon-class submarine TK-208's fire extinguishing system is triggered due to a electrical malfunction, pumping freon gas into three of the submarine's compartments. Several dozen crewmen are asphyxiated, and before control can be restored, the submarine crashes scrapes an undersea peak, rupturing two of the hulls, and flooding several compartments. The surviving crew manage to secure the rear-compartments, but few of them survive for the three days it takes for rescuers to arrive, a delay later attributed suspicions that the distress signals received were part of a NATO ruse.
Result: Construction of the remaining Typhoon class submarines is halted while a full investigation is performed. KGB Chairman Yuri Andropov handpicks the KGB investigators, whose secret report exonerates the Secretary Ustinov and other allies of Andropov, while pinning most of the blame on "laxity" within the Soviet Navy's submarine docks. The launch of the next Typhoon-class submarine in delayed 2 years. This possible scrapping of the "Akula" class submarines leads the USN to delay the start of its replacement for the Los Angeles Class submarines.