I am not sure I would use the word mistakes. Britain, the USA and the Soviet Union were allies during the war, although I would use the word ally loosely for the Soviet Union. The SU had a plan - and it wanted a greater sphere of influence in Europe and Churchill -- and Churchill (Roosevelt was not a well man) allowed it to happen. FDR wanted Soviet Support for an invasion of Japan -- and the Soviets wanted territory in Europe for their own security - ie, what would become the Eastern bloc. If I recall, Churchill demanded that the Soviets allow for free elections (which didn't happen). The Soviets were very close to getting to Berlin by that time. Here is a good explanation of Yalta http://www.cnn.com/SPECIALS/cold.war/episodes/01/documents/yalta.html

Zahir Shah had been overthrown in 1973 when he was in Rome -- a cousin was responsible, and within several years, a republic was established. In 1979, in a carefully orchestrated plan to wide the sphere on the Central European/Asian borders, the Soviets moved in, and began a process that would further destabilize the region, allowing for the Taliban to move in.
As for King Peter - well, he would never have survived as king in Yugoslavia. He was a child when his father was assassinated. He grew up as king during a regency. He was against the tripartite agreement that allowed for German troops to move in - but there was nothing that he could have done about it - to prevent it. His education was limited. He loved his country and he wanted to take part in the fighting there, but Churchill would not allow it ... Churchill knew that Tito had the power to rule the country - and Peter would never have survived. Sadly - and tragically - Peter's post-1945 life was full of pathos and drama. I don't think the US is inherently against kings - Truman honored KIng Michael - but unfortunately, the US and the UK could do very little to protect his throne as Romania had become a part of the Soviet sphere of influence.
It would have been nice if the Britain and the USA had been able to persuade the Soviets to allow free elections, etc., but the Soviets had their own plans, regardles of what they said at Yalta.