I want some recommendations on things to read, tutorials, etc on PTC WindChill.
And know your opinion about them.
Also I'd like you to tell about any tricky problems or things or common pitfalls.
It depends on what you intend to do.
WindChill is a huge system made of several components (a PDM database, an application server, the Info*Engine web framework, etc.), so you must first have a basic idea of what you want to be able to do with it (try to get some use cases for example).
Then, since it is a proprietary system targeted towards a really specific market (PLM), the best way to get started is to get a training course directly from PTC or one of their local partners.
That's what I've done, and I was pretty pleased to learn that I needed to know a really small fraction of the whole system to get things done for my needs, using just a few HTTP GET requests.