Not something you'd use all the time and you need to know how to use the command-line, but there is the fs_usage command. You need root/admin privileges to run it but it shows you all filesystem activity. You can have it filter by program.
Having Hazel monitor everything may be a bit much. First off, it would probably require admin/root privileges which is not something I want to require. Also, the possible resource drain (running fs_usage, you can see how much data must be sifted through). But, I think the main problem is that while you see every file an app creates, you don't know for what purpose. It's unclear whether you can really differentiate between files the app creates for it's own internal storage and files the user creates using that app. For instance, if you are using an image editor and create a JPG file, that's not a file you would want the uninstaller to remove but it will be recorded as a file created by that app. The chance of a false positive goes up using this type of approach.
As for the problem removing Cha-Ching, check the logs. You can view them via the "Check Log" button in the "Info" section. See if there is a more descriptive error. My guess is it's a permissions problem. Post here or email me if you can't figure it out.