I know about the aerial engagements over Vietnam, but were there any incidents in other places where it became public knowledge?
Probably not the only incident, but definitely the most high profile, was the death of Major Arthur Nicholson, an officer in the US Military Liason mission to the Group of Soviet Forces in Germany, who was shot by a Soviet sergeant while attempting to spy on a Soviet military facility in the DDR.
[Here] (http://www.nytimes.com/1988/06/15/world/soviets-offer-apology-in-killing-of-us-major.html) is a link to a NY Times article about the Soviets' formal apology for his death (which came three years after he was actually killed).