I would do a few things:
1) simulate user/application connection to the db and test load (load testing).
I would suggest connecting with many more users than are expected to actually use the system. You can have all your users log in or pick up third party software that will log in many many users and perform defined functions that you feel is an adequate test of your system.
2) insert many (possibly millions) of test records and load test again.(scalability testing). As tables grow you may find you need indexes where you didn't have them before. Or there could be problems with VIEWS or joins used through out the system.
3) Analyze the database. I am referring to the method of analyzing tables. Here is a boring page describing what it is. Also here is a link to a great article on Oracle datbase tuning. Some of which might relate to what you are doing.
4) Run queries generated by applications/users and run explain plans for them. This will, for example, tell you when you have full table scans. It will help you fix a lot of your issues.
5) Also backup and reload from these backups to show confidence in this as well.