PDF is an extremely complicated document file format, with enough tricks and hiding places to write about for years. This also makes it popular for CTF forensics challenges. The NSA wrote a guide to these hiding places in 2008 titled "Hidden Data and Metadata in Adobe PDF Files: Publication Risks and Countermeasures." It's no longer available at its original URL, but you can find a copy here. Ange Albertini also keeps a wiki on GitHub of PDF file format tricks.
qpdf is one tool that can be useful for exploring a PDF and transforming or extracting information from it. Another is a framework in Ruby called Origami.
When exploring PDF content for hidden data, some of the hiding places to check include:
Adobe's metadata format "XMP"
the "incremental generation" feature of PDF wherein a previous version is retained but not visible to the user
white text on a white background
text behind images
an image behind an overlapping image
There are also several Python packages for working with the PDF file format, like PeepDF, that enable you to write your own parsing scripts.