Obvious evidence connecting the murder of the Pope to the Soviet Union?
A lot of people in otherwise 'neutral' Catholic nations are going to be pissed. John Paul's successor may well put the Soviet Union under a Papal Interdict. It may not do much, of course - Venice managed to laugh off an interdict back when the Church had real temporal power - but this is essentially the Soviet Union declaring war on the Catholic Church.
Poland is going to be very messy. The Soviets may well crush the resultant uprisings, but there sure as hell are going to be uprisings. There might be uprisings in other communist Eastern European countries with large catholic populations as well - Czechoslovakia and Hungary, basically.
A lot of communist and other leftist organizations in Latin America, if they haven't already, will drift from Soviet influence and ideology and become more Maoist or Titoist, and forswear any connection to the Soviets.
A lot of leftist organizations in Latin America tend to connect themselves more with Catholicism, and vice versa - "Liberation Theology" and all - and while they tended to be ideologically opposed to John Paul's more conservative brand of Catholicism, they will not be happy with the pope being assassinated.