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One thing that is different because he is a CEO of a publicly traded company is that there are regulatory requirements, so his "qualifications" are submitted to the SEC (at least, I think it would be the SEC, but maybe it is the FTC). Another thing that this highlights, as articulated by Warren Buffet, is that "Yahoo has a trust problem." Among others, I might add.
It is surprisingly common for people to augment their resumes. There was March 3 article in USA Today that stated ~35% of resumes contain lies about education, skills or experience. If that is accurate, there are a lot of people that are hired based on false information, and that could have a serious impact on an employer. You wouldn't want to have a conversation a few months after a hire that starts with, "I though you knew how to run a nuclear power plant...."
I suppose that it is inevitable, especially in a job market where highly qualified people can find it difficult to get a job. It is very difficult for most companies to thoroughly check resumes of potential hires for falsification, so there is a pretty good chance that many people will get away with it. Maybe not if you are the CEO of a huge company though.
Oh, and I think Yahoo has two options, claim it was some secretary that made an error, or can Thompson. The window has pretty much closed on that first option though. I think it damages the company image to keep him on board, and the issue isn't going away. On the other hand, they look like a bunch of idiots if they fire their new CEO.