What are the most difficult sample matrices to extract high quality DNA from using current extraction technologies (spin columns/bead extractions) in which PCR inhibitors are a large problem?
Your question is really broad. It is likely that anybody can come with a diffrent sample which is difficult to handle. As an example, plant samples are known to be problematic because they carry phenolic compounds (among others) which interfere with downstream applications. There are workarounds and custom steps to reduce these compounds during extraction (Bmercapto, PVP...).