In storing passwords in a database should I use a per-application salt in addition to a per-secret salt?
There is an advantage.

Cracking a password from its hash without knowing the salt is extremely difficult, as you're essentially increasing the password length by the length of the salt.

If you're storing the hash in such a way that it isn't obvious that it's been salted by the application, the attacker likely won't go looking for it. If the application itself isn't plain text (ie; compiled in some way), even if they do go searching for it, it is non-trivial to find.