A number of people have posted long lists of supposed reasons why the GFDL is not a free license. I have not seen one that is valid, but I cannot comment on each point. It takes longer to refute an attack than to make one, and the critics outnumber me. Even supposing I could afford to spend full time on this discussion, I could not keep up with them.
Instead I am addressing the broader issues that underlie many of the objections, using particular examples as appropriate. Many of the objections to the GFDL are based on a specific kind of exaggeration: pointing at an inconvenience and calling it an impossibility. Here is one example: I wanted to make a BSD DIFF manual by editing the GNU DIFF manual, but I *couldn't* I believe he can. (cover texts say "GNU" which wouldn't be accurate). The cover text says "A GNU Manual". This would be a modified version of a GNU Manual, so I think the statement is accurate enough. The requirement for these cover texts does not stop him from adapting the GNU Diff manual to make the "BSD Diff Manual". Substantively, he is free to make these modifictions, but there is a requirement on how to package them. A requirement on how to package a modified version does not make a license non-free. The point is that people are free to make the substantive changes they want. Many free software licenses have requirements for packaging modified versions. If we removed all parts of the system whose requirements on packaging are distasteful to some, little of the system would remain.