My copy of the 1st printing of the 5th edition Player's Handbook certainly started falling apart after light use. Basically folio-like "chunks" of about 15 or 20 pages of the book separated cleanly from what looks like some kind of heat-set plastic binding glue. This happened to me twice in two different parts of my book, and the first time the separation only happened toward the top, but the "chunk" remained attached at the bottom. The second time, the "chunk" was almost entirely unattached, top to bottom.
Fortunately, if you are in a similar scenario it is not too difficult to repair your copy of the PHB, as the pages come out so monolithically en masse. To repair:
- Get some Gorilla Glue, a pin or needle, a piece of cardboard or paper to serve as a place to hold glue while you work, and have about 20 minutes;
- dollop the glue onto the cardboard;
- open the book wide, and with the pin scoop a small drop of glue from the dollop, and with the pin smooth a very thin layer back and forth across the width exposed binding glue in small swatches, patiently working your way the entire length of the seam (the narrow size of the exposed original binding glue and the thick consistency of the Gorilla Glue prohibited doing this with a brush);
- push and massage the neatly stacked pages into place until they are flush top, bottom and outer margins; and
- close the book and place it under weights—say, a pile of 1st-4th edition D&D books ;)—as it dries. Gorilla Glue, once activated by the water in the air, takes about 4 hours to cure, so I would just leave the book pressed under weight overnight and you are all set.
I did this repair months ago, and have been using my 1st printing of the 5th ed PHB pretty heavily since, and it is working very nicely. So nicely, in fact, that you cannot tell that there was ever a problem with the binding. Again: go very thin with this glue, as it will expand and foam if you go at all thick, and do not get it on anything but the old binding glue.
Caveat for the book binding nerds: Yes, I know Gorilla Glue is not a good book-binding glue in general, and when I perform a new bind I do not use it. But this is a very specific repair—some sections falling out, and not even entirely out—on specific materials. :)
Update 5-5-16: For those wondering about how this repair holds up under heavy use: the PHB has held up beautifully with the repair job I described in this answer to date.