In the final-system build, you are no longer cross-compiling so it is possible to run package testsuites. Some test suites are more important than others. For example, the test suites for the core toolchain packages—GCC, Binutils, and Glibc—are of the utmost importance due to their central role in a properly functioning system. The test suites for GCC and Glibc can take a very long time to complete, especially on slower hardware, but are strongly recommended.
A common issue with running the test suites for Binutils and GCC is running out of pseudo terminals (PTYs). This can result in a high number of failing tests. This may happen for several reasons, but the most likely cause (if you chrooted) is that the host system does not have the devpts file system set up correctly. This issue is discussed in greater detail at http://trac.cross-lfs.org/wiki/faq#no-ptys.
Sometimes package test suites will fail, but for reasons which the developers are aware of and have deemed non-critical. Consult the logs located at http://trac.cross-lfs.org/clfs/build-logs/svn/ to verify whether or not these failures are expected. This site is valid for all tests throughout this book.