I want to add a password blacklist that would prevent the 1000 most common passwords from being used in order to mitigate shallow dictionary attacks. Is there any negative implication of storing this blacklist in the database?
In that order of magnitude (1000 passwords), I don't see any down sides from a security point of view. If anything, I'd say it's a good idea. Granted, you'll be shrinking the pool of possible passwords which, theoretically, decreases the security. In practice, however, those most commonly used passwords will be one of the first wordlists an attacker would try.
In fact, I've seen a few web services disclosing this in their registration forms. Some even block whole dictionaries in addition to common passwords.
Not only is this not a bad idea, it's actually quite advisable. In fact, there's a whole library already included on most Linux/Unix systems called cracklib which helps you prevent users from picking horrible passwords.
There are bindings for this library in most languages, which makes checking for bad passwords pretty trivial. You just say "cracklib, is this password bad" and it will say something like: "this password is based on a reversed dictionary word".
From a security perspective, there should be no negative implications. The only thing I can think of will be the attacker knowing not to try those 1000 passwords if he manages to get hold of that list but that's really doesn't count.
I can see one problem in this situation, it will make brute force easier for the attacker. They will have fewer passwords to try in order to break into the account. I think you should not limit password choice to users at all.
If you make the blacklist public and it has your boss's favorite password CarlosDanger77 in it; chances are you are getting canned when his Twitter account gets hacked with it.