If you think the lib is buggy, please read first the FAQ. It might be that others had the same problem and there's an easy solution. You should also check the section "Recommended Tools to Install the GNU C Library" in the INSTALL file since some bugs are bugs of the tools and not of glibc.
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.
Next, go to http://www-gnats.gnu.org:8080/cgi-bin/wwwgnats.pl, and look through the bug database. Check here to verify the problem has not already be reported. You should also look at the file BUGS (distributed with libc) to check for known bugs.
Once you're sure you've found a new 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. When reporting a bug, send your test case, the results you got, the results you expected, what you think the problem might be (if you've thought of anything), your system type, the versions of the GNU C library, the GNU CC compiler, and the GNU Binutils which you are using. Also include the files config.status and config.make which are created by running configure; they will be in whatever directory was current when you ran configure.
All bug reports for the GNU C library should be sent using the glibcbug shell script which comes with the GNU libc to [email protected] (the older address [email protected] is still working), or submitted through the GNATS web interface at http://www-gnats.gnu.org:8080/cgi-bin/wwwgnats.pl.
Suggestions and questions should be sent to the mailing list at [email protected]. If you don't read the gnewsgroup gnu.bug.glibc, you can subscribe to the list by asking [email protected].
Please DO NOT send bug report for the GNU C library to <[email protected]>. That list is for bug reports for GNU CC. GNU CC and the GNU C library are separate entities maintained by separate people.