regrtest already tests for refcount leaks and memory allocation leaks.  It can also be made to check for file descriptor leaks (and perhaps also handles on Windows).

Running with the attached patch makes it look like test_openpty, test_shutil, test_subprocess, test_uuid all leak fds on Linux, but I have not investigated:

$ ./python -m test.regrtest -R 3:3 test_openpty test_shutil test_subprocess test_uuid
[1/4] test_openpty
123456
......
test_openpty leaked [2, 2, 2] fds, sum=6
[2/4/1] test_shutil
beginning 6 repetitions
123456
......
test_shutil leaked [4, 4, 4] fds, sum=12
[3/4/2] test_subprocess
beginning 6 repetitions
123456
......
test_subprocess leaked [5, 5, 5] fds, sum=15
[4/4/3] test_uuid
beginning 6 repetitions
123456
......
test_uuid leaked [1, 1, 1] fds, sum=3
4 tests failed:
    test_openpty test_shutil test_subprocess test_uuid