This is kind of silly but you can't currently see your version number from within ListMail.. What you need to do is look at the top of the admin.php file.
About line 6 you will find the line:
$current_version = '1.77';
Note that this is simply the version of the database, not necessarily the files. v1.77b, now available from the member area, is basically v1.77 with a few fixes and improvements.
Tip: If you're not sure if you have the latest files, simply do an update with the currently downloadable ZIP. Replace your main ListMail files, except config.php, and re-login to the program. Your data will not be affected.