I agree with the influence of all you've listed above, and any are good choices for
Person of the Century.
I'm inclined to say
Adolf Hitler for Man of the Century. Not out of any affection for Hitler, just based solely on his impact on an entire century.
Hitler's opinions were based on the antisemitism and anti-semitic publications prevalent in the late 19th/early 20th century in Europe, North America and elsewhere, that Hitler grew up reading.
Hitler fought in WW I, and he increasingly became a voice for the German man on the street, and for German humiliation and lost pride from 1921 till 1934, when he gained absolute power over Germany.
Hitler took a war-torn, humiliated, and economically destroyed country, and within a few short years made it once again an empire, a global power, and if not for Hitler's own mistakes, Germany was poised to seize the world.
In the aftermath of Hitler, Europe and the rest of the European colonial world (who shared similar segregationist/subordinate attitudes toward blacks, Jews and other non-European races) took a different turn, toward greater rights and equality, in opposition to the Nazi practices the allies had fought against.
And more pragmatically and less idealistically, Europe had exhausted its power warring against itself in WW II, and could no longer hold onto its colonies outside Europe, even if it wanted to. And all these nations in Africa and Asia gained their independence within a few short years as a result.
Without Hitler, colonialism might have gone on forever. Or at least a very long time.
Without Hitler, the post-WW II world would not have shaped into a global balance of power that has bred stability and remarkable peace for the last 60 years, and the greatest economy and standard of living the world has ever known.
But the counter-argument to selecting Hitler as most influential is:
at what price?
Certainly, Hitler is directly responsible for the deaths of at least 20 million people. But both directly and through indirect long-term ramifications, Hitler's influence on the entire world has been tremendous.
Others whose influence I could easily argue for are:
Franklin D Roosevelt (who more peacefully did many of the same things for the United States that Hitler did for Germany, with a more enduring legacy for the U.S., and interestingly, Roosevelt was in power the exact same years, almost to the month, as Hitler, from January 1933 to April 1945. ),
Winston Churchill (who, even though he had nothing left to fight with, inspired England to resist Hitler and remain sovereign. And is one of the most eloquent speakers of the 20th century),
Joseph Stalin (for many of the same reasons as Hitler. Stalin, and reaction to Stalin, re-shaped the world into its present form, but at an enormous human cost)
Ronald Reagan (who by "peace through strength" changed the landscape of Europe and Russia, without a shot being fired, and who inspired the U.S. to rebuild itself from within, economically, militarily, and spiritually, and restored the U.S. as a great nation again )
For the 21st century, I'd pick
Bill Gates, for the innovations that have united the world economically, and revolutionized commerce and communication.
To answer your second question, Rob, I have no problem with an entertainer being selected as person of the century.
Although more subtlely, entertainers change the world too, inspire us, and unquestionably make the world a better place. I think part of Reagan's appeal (and Schwarzenegger's as well) is that they
are entertainers, beyond their other achievements.
Elvis arguably unites the world, as do The Beatles, Madonna, U-2, and many others. As do Jack Kirby comics, Disney movies, Humprey Bogart, Clint Eastwood, Julia Roberts, Meryl Streep, and a million other entertainers with their creations.
These shared cultural icons give a common experience to people of vastly different cultures.
And that, no question, brings the world together and makes it a better place.
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"This Man, This Wonder Boy..." 
