* Make your own Penn State/State Pen joke. *
As those who know me know, I am not a sports fan and tend to think of anyone involved with such as more likely of being guilty of something than the averages of probability would indicate. Note that I am not defending what happened. I am explaining how I think the failure mode worked.
Joe Paterno was, from what I can tell, the guy that all the stuff about "good sportsmanship" was about. He didn't jump to the NFL when offered the chance. He didn't use illegal or even questionable recruiting gimmicks. He followed up on the academics of his players. Oh, and he also managed to build teams that tended to win without having used various shady practices. Sounds like a great guy, right? Overall he likely he is. But he made a couple errors, very critical errors, and they really reduce to one.
One error was that when he found out about the abuse (as I understand it, he did not witness it himself, but was told of it) he went to campus authorities rather than the real police. The other was that he didn't follow up on that, as he did with his players, and make sure that those authorities were really doing their jobs and acting on that information rather than ignoring or suppressing it. Those are really one error: He trusted University authorities to act as adults and do their jobs. For all I know, there might have been a mild followup that was met with, "We're still looking into it, don't worry about it." or such. It would not surprise me if something on the order happened - but that is mere speculation on my part.
But money and prestige were involved, and that's when adults are most likely to play childish (not childlike) games and ignore or suppress things they do not wish to deal with. The price is that now there is a Big Scandal of things going on for some time, involving multiple people, rather than a much smaller scandal that Got Fixed. People keep forgetting or missing a lesson of Watergate (besides "Don't do illegal things"...) which is that a coverup makes things worse. But the big lesson that should be taken away from all this? Do not trust an organization to properly investigate itself. To get results, you must go outside the organization that needs investigation. Sadly, I do not expect this to change and in a while another scandal that could have been averted or corrected sooner will blow up.
 I've seen it put, "Nixon didn't resign because of a break-in; he resigned because of a coverup."