Libtool comes with an integrated set of tests to check that your build is sane, that test its capabilities, and report obvious bugs in the libtool program. The test suite is based on Autotest from Autoconf (see Generating Test Suites with Autotest in The Autoconf Manual). These tests, too, are constantly evolving, based on past problems with libtool, and known deficiencies in other operating systems.
As described in the README file, you may run make -k check after you have built libtool (possibly before you install it) to make sure that it meets basic functional requirements.