The previous answer does a good job of outlining some major successes and failures of that time. I'd just add this:
I do not think you can talk about the successes of the early part of this period without talking about "De-Stalinization." Up until Khrushchev came along, the terror that Stalin had unleashed had killed millions and condemned millions more to prison. Khrushchev came in and put an end to forced labor (for people other than prisoners). He also freed millions of people from the prisons on the idea that Stalin had gone overboard in his attempts to prevent people from disagreeing with him. By doing these things, Khrushchev improved the lives of Soviet citizens.
Sadly, this also led other countries in the Communist bloc to think they could get away with pulling away from the Soviet Union. Both the Poles and the Hungarians tried this and it led to the Soviets' brutal repressiong of Imre Nagy and his reforms. You'd have to say that reaction to Hungary was a failure, at least in moral terms."
In such a response, there would have to be detail and specific supports with historical reference in order to be a part of a serious form of writing. Yet, there can be some broad points made as to successes and failures. One such success for the Soviets would be the launch of the Space Race with the Sputnik satellite launch in 1957. At this particular moment, the Soviet Union was seen as world force of space exploration and enjoyed the credibility that came along with it. Certainly another positive, at least internally, could be the escalation of the Cold War. During the time period, the Soviet Union matched the United States in terms of intensity regarding the battle of ideologies and there was little in terms of surrendering. Another positive success could be seen in Soviet intervention in Vietnam. Perhaps taking a cue from the Americans, being embroiled in such a conflict would have proven to be disastrous. The Soviets provided weapons and military equipment, but managed to keep casualties to a very low number. Even though it was revealed later on that the Soviets had 3000 troops stationed in Vietnam, the reality was their number of dead and wounded was astonishingly low, contributing to an overall perception that they handled the conflict better than the superpower counterparts. Finally, the American frustration in Vietnam led to the Soviets being perceived as being the Superpower with greater control and stability throughout the 1970s. When Brezhnev negotiated the SALT treaties with Nixon, it seemed that the former was doing so out of a position of power, while the latter was grasping at straws, trying anything to offset the negative image of Vietnam.
There were some missteps of the Soviets. Kruschev endured much in way of domestic criticism for his poor handling of the Cuban Missile Crisis. Additionally, the Soviet response to the crisis helped to erode the base of good will relationship between Cuba and the Russians. At the same time, much can be made about how the Soviet Union focused all of their national agenda on defeating the Americans, and not developing infrastructure and creating economic inroads on a domestic level. Part of Russia's crippling economic status today was because of a lack of internal growth and development during the years that followed the Second World War. Finally, the Soviet invasion of Afghanistan could not be considered a success, as it helped to destabilize the region, enhance the perception that would be fed later on that Western nations viewed Asian ones with disrespect, and helped to mobilize the Mujahadeen and one of their generals, Osama Bin Laden.