When the tests in the old test suite are run via make check, output is caught in per-test tests/test-name.log files and summarized in the test-suite.log file. The exit status of each program tells the Makefile whether or not the test succeeded.
If a test fails, it means that there is either a programming error in libtool, or in the test program itself.
To investigate a particular test, you may run it directly, as you would a normal program. When the test is invoked in this way, it produces output that may be useful in determining what the problem is.
The new, Autotest-based test suite produces as output a file tests/testsuite.log which contains information about failed tests.
You can pass options to the test suite through the make variable TESTSUITEFLAGS (see The Autoconf Manual).