The fatal shooting of an American officer in East Germany last Sunday violently marred one of the most smoothly functioning relationships between the United States and the Soviet Union: administering their vestigial occupation rights in Germany. The carefully tempered anger of the United States over the killing of Maj. Arthur D. Nicholson Jr. by a Soviet sentry appeared to suggest a wish to contain the incident and not allow it to disrupt the arms talks.

Similarly, Western diplomats noted that - in contrast to the adamant position taken on the downing of a South Korean airliner in 1983 - the Soviet Union had expressed ''regret'' over the slaying even while accusing the officer of having taken pictures inside a restricted military area.

Responses Were Restrained

The calibrated responses of both sides were typical of their daily dealings in observing agreements arising from their roles as onetime allies who defeated and occupied Nazi Germany.

While little known, these arrangements are vital to the hold of the United States, Britain and France on West Berlin, isolated within East German territory. They are also significant for the Soviet Union in justifying its military presence in East Germany.