An opinion is a sentence that has the function to state a personal position about a certain matter. It generally reveals the truth from a person's (or a group of people) understanding and ideas about something, based on this person's (group of people) feelings and beliefs. It may not necessarily be a proven fact.
So, taking this in consideration, analysing sentence by sentence, we have:
Nancy couldn't make it today because she's visiting Leningrad - Fact.
One of these chips has more computing power than a roomful of old-style computers - Opinion!
<em>Although President Reagan is stating a precise sentence, an apparent 'fact' here, it is not a </em><em>proven</em><em> fact. </em>
But progress is not foreordained. - Opinion.
<em>He's clearly stating his idea about 'progress'.</em>
The key is freedom—freedom of thought, freedom of information - Opinion.
<em>Again his idea about what 'the key' would be.</em>
You know, one of the first contacts between your country and mine took place between Russian and American explorers - Fact.
<em>Although not entirely precise, he's stating something that is generally believed to be true.</em>
Perhaps most exciting are the winds of change that are blowing over the People's Republic of China - Not an opinion nor fact.
<em>He's not saying a complete trustworthy information here, but he's not also demonstrating a straight opinion either. When stating something that may or may not be true (through the 'Perhaps', in this case), you are in a certain way saying that you </em><em>don't have an opinion about that yet</em><em>, but you're provoking a discussion (or at least the thoughts) towards one.</em>
And that's why it's so hard for government planners, no matter how sophisticated, to ever substitute for millions of individuals - Opinion.