Using a server-wide salt value for all passwords is akin to wrapping your bullet-resistant glass in cellophane. You’ve just taken a reasonably strong, industry-standard security measure and wrapped it in the naivest possible form of security, the good ole’ hard-coded password.
Random salts are intended to prevent a dictionary attack. Nothing more, nothing less. To accomplish this, as well as the side benefit of defeating rainbow tables, they do not need to private or cryptographically strong. It also does not matter if the salt is appended, prepended, or randomly distributed within the original password, as long as the process is repeatable. The point is, if two users have the same password (something crackers frequently try to make use of), they won’t have the same hash. And if someone wants to run a dictionary or even a brute-force attack, they now have to re-run it for every single user.
Most importantly, if you’ve secured your database properly and your hacker does NOT have direct access to every password, then they may try to sniff the password over a network, and assuming your security takes replays into account, a random salt makes the sniffed hash much more difficult to use. I suppose a constant, hard-coded salt provides some security here - unless the hacker happens to be a disgruntled ex-employee who knows what it is, which is actually the most common cause of espionage.
By all means, secure your salts too if you’re paranoid. Put them in a separate table or a separate database or even a separate server. Or even better, use a nonce, or a much stronger scheme like Kerberos. It can’t hurt. But a global hard-coded shared secret is no substitute for a random salt. It’s a feel-good measure, effectively useless and bordering on superstition, but enough for someone to give himself a pat on the back for being more secure.
If you want to be really clever about your salts, then don’t just stick them at the beginning or end; use an algorithm that distributes the salt characters within the original password in a way that’s dependent on the password itself. That way, a 10-character salt is essentially useless to anyone who doesn’t know the distribution algorithm. You’ll get all the benefits of secrecy without sacrificing the security itself.