What I have read indicated that Paterno was advised of something that a then-graduate assistant claimed to have observed. I think that is a stretch to say that he "knew of specific incidences within the PSU facility." He was advised of what someone told him. How did Paterno know whether that GA was telling the truth or not? Maybe the GA couldn't stand Sandusky. Maybe the GA was trying to get rid of Sandusky. Maybe the GA was trying to stir up trouble within the Penn State coaching department. 2nd hand information is generally not reliable - there is a reason it is called hearsay.
Joe Paterno is not a police officer. Joe Paterno did not personally observe any wrongdoing (at least as much as I've seen reported). He received information 2nd hand. With the information he was provided, Joe went up the chain of command, as was the policy of Penn State University, and told his superiors what had been reported to him. Could Paterno have done more? Sure. But I think it is a stretch to suggest that he had some type of "moral responsibility" to do more -without more information to support it. I will say -- if this was not just an isolated event (i.e. if Paterno had been told about other incidents involving Sandusky before this GA information) I think he has an obligation to do more.
I am sure we have all been told of "rumors" of wrong-doing before. Everything from extra-marital affairs to knowing a friend was drunk driving to knowing a friend stole office supplies from his workplace. As an attorney I have certainly heard reports of illegal activity. I don't think anybody is under a "moral obligation" to start calling police unless that person has actual personal knowledge of the wrongdoing, or a reason to suspect wrongdoing. The mere fact that someone claims to have observed some wrong-doing is not enough, imo. If I called your boss and told him I had seen you doing something illegal (something I totally manufactured on my own) -- would my comments, alone, warrant a full police investigation into what could be nothing more than my made-up allegations.
There needs to be a more thorough investigation into just what happened at Penn State when all these things unfolded. At the end of the day it is still a public university and every employee is entitled to certain due process. It is an unfortunate situation, but it is all too easy to look back today, almost 10 years later, and say that you would have acted differently.