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I've upgraded my Macbook Air since Lion without issue. There's no reason to expect trouble coming from the new security features as homebrew/macports as well as sane make scripts default to installing outside system directories anyway. In the worst case, you'll just have to reinstall the offending applications.

Of course you still do a backup before in case the universe blows up.

These fast thinking problems rely on pattern recognition, so they will be easy if you have already seen the pattern, but you will fail if you apply the wrong pattern. Problem 3 tricks people who are used to everything being linear, which would probably be rather few people on HN.

I think the important skill is to be on the lookout, in your fast thinking, for problems which are slightly off. This is a clue that the pattern doesn't fit, and you should revert to slow thinking.

I think the quality of numberphile videos vary quite considerably. The one you linked is a rather honest explanation of the idea of comparing the size of sets through bijections and a good explanation of Cantors diagonal argument. As a mathematician I'm quite fine with it.

The one linked in the submission is more of an obvious statement hidden by obscure use of language. Slightly silly, but not very bad.

The worst offender with "magic" is the one with the Riemann zeta function [1], which went viral a while ago. The problem here is that they get people started off on the wrong foot, confusing them with wrong arguments and hidden definitions. Now, if people really want to understand why this can be made meaningful, you first have to explain that the better portion of the video is absolutely wrong, and only then can you explain what is actually going on.

[1] http://youtu.be/w-I6XTVZXww