What you should be careful about is the things surrounding the database: the .php files (or whatever) that read/write the database, and the system it is running on.
Basic security practice for the web: NEVER trust user input: check and recheck all the GET/POST variables, check that numbers are numbers, that strings are correct strings (they have no funny characters, such as " or ; (for databases) or <>"&' (for HTML) or . (for paths)). Check all input into the databases (to prevent SQL injections) and all output for to the user (for XSS).
Basic security practice for sysadmins: Use up-to-date OS and software. Use strong passwords. Almost never run root. Make remote access hard.
This seems easy, and for the most part, it is. It's just so many things that people forget to check for them all.