Make sure to get all the "gotchas" for the application. They are often the data or business items that are too minute or quirky to have formal documentation, but wind up having big impacts or lots of debug time if you don't know what's going on.
For instance, in one of the applications I currently maintain, we interface with a third party system that has a "web viewer" type client. The "gotcha" with this is that the web viewer doesn't properly maintain the user's session state (broken when it was updated to their latest version to fix other critical issues). As a result, I have to remind the users from time to time to simply minimize the browser window so that the timeout occurs naturally, otherwise they will get locked out for a prolonged period of time until the Ops folks around here get the newer version installed.