I know this is an ancient thread, but I was reviewing it as I too was recently having a problem like this.
In my case, most files students were downloading were corrupted. It turned out that the problem was an intermediate reverse proxy server. The reverse proxy server's root partition had run out of space and in turn it was only able to handle quite minimal connections. As soon as we cleared out some space, sanity returned.
Funny thing is, I've been rolling out Nagios deployments monitoring my networks, but had yet to apply it to this one, it would have caught this issue immediately!
I hope this post helps someone.