There was at least one: the famous Stanislav Petrov incident in 1983, where a Soviet early warning station misinterpreted sunlight bouncing off of clouds as incoming missiles. Petrov, the officer on duty, dismissed it as being probably false, and did not report it. It came at a time of significant tension and suspicion by the USSR that the US was planning a surprise first-strike attack, so it was not an insignificant affair.

Were there more from the Soviet period? I haven't seen any description of them. There likely are — these are not artifacts of "bad technology," they are just the result of large, complex systems that will inevitably have a few bugs in them. In the United States we have a pretty decent record of these because the US is comparably open about its nuclear work compared to other countries (the Soviet incident did not surface until the 1990s, and only because of the people who knew about it wrote a memoir). The US also deployed many such systems, and hastily and redundantly, thus increasing the chances of malfunction, but the experts I know suspect that the reason we don't hear about nuclear incidents and accidents in other states is not because they don't happen, but because they don't talk about them.

On the Petrov incident, David Hoffman's The Dead Hand has a nice account. On the causes of accidents more broadly, Schlosser's Command and Control is readable and fun, and Perrow's Normal Accidents is a good starting point for "accident studies" (why they happen in complex systems, etc.).