I actually ended up working on a completely different project but I had to periodically build a useless calculator using jQuery Mobile in the corporate colors and present it to our completely useless VP of IT.
He had sold the company's leadership on the absolute necessity of a mobile presence, that this effort needed to be completed post-haste and how it would dramatically increase sales (most of the company's business was selling insurance to other financial firms, almost no consumer products in their portfolio).
In my first meeting with him he told me he wanted "MSN Mobile for an insurance company" and offered no other instruction. He literally pulled up m.msn.com on his iPhone and said to make a version of that as their mobile presence. After that meeting I just hid in my cube and laughed for a few minutes. That was when I realized what a farce this effort was.
Basically the entire development team knew how pointless this was but the VP had sold it to the rest of the execs and now they needed to build it. No one wanted to put in the effort. The created the internship position so they could foist the actual coding off to an unsuspecting college student (me) while actually having him work on an unrelated but useful project.
Didn't learn much about coding (VB.NET, ugh) but the experience in how a bad company works? Invaluable.