There are probably bugs in the GNU C library. There are certainly errors and omissions in this manual. If you report them, they will get fixed. If you don't, no one will ever know about them and they will remain unfixed for all eternity, if not longer.
It is a good idea to verify that the problem has not already been reported. Bugs are documented in two places: The file BUGS describes a number of well known bugs and the bug tracking system has a WWW interface at http://sources.redhat.com/bugzilla/. The WWW interface gives you access to open and closed reports. A closed report normally includes a patch or a hint on solving the problem.
To report a bug, first you must find it. With any luck, this will be the hard part. Once you've found a bug, make sure it's really a bug. A good way to do this is to see if the GNU C library behaves the same way some other C library does. If so, probably you are wrong and the libraries are right (but not necessarily). If not, one of the libraries is probably wrong. It might not be the GNU library. Many historical Unix C libraries permit things that we don't, such as closing a file twice.
If you think you have found some way in which the GNU C library does not conform to the ISO and POSIX standards (see Standards and Portability), that is definitely a bug. Report it!
Once you're sure you've found a bug, try to narrow it down to the smallest test case that reproduces the problem. In the case of a C library, you really only need to narrow it down to one library function call, if possible. This should not be too difficult.
The final step when you have a simple test case is to report the bug. Do this using the WWW interface to the bug database.
If you are not sure how a function should behave, and this manual doesn't tell you, that's a bug in the manual. Report that too! If the function's behavior disagrees with the manual, then either the library or the manual has a bug, so report the disagreement. If you find any errors or omissions in this manual, please report them to the bug database. If you refer to specific sections of the manual, please include the section names for easier identification.