There's really nothing that will clean any residual files from deleting apps (if there is any, by the way). Apple is pretty protective of the "sandboxed" system, so I'm not surprised about that. In addition, the iPad is not like a computer in that you don't do the kind of systemic clean-up you might do every now and then on a PC.
You can, however, use an app to help you clean out the RAM [faster]. A lot of people like to use XSysInfo, which has been updated and provides memory "boosting" (it cleans RAM).
However, cleaning RAM can also be accomplished by either restarting or rebooting the iPad, so it's a toss-up as to whether you want to buy an app to do the same thing.
Last - if you really think you need to "clean up" the iPad, you can always do a restore on it (where you wipe out the operating system, install a clean version and then reload your apps). That's rather drastic for what some would think is an unnecessary step. YMMV.
Hope that helps/makes sense.
Marilyn