Installation/Uninstallation is tricky a lot depends on the context.
What operating system does it target?
Where does that OS store Temporary files?
Where does that OS store user data?
Where does the installer store the primary 'files' for the system?
Where does the installer store common or shared files?
Does the system store data in a user folder?
Does it interact with an application manager of some kind?
Does it install into the registry (Windows)?
When it uninstalls does it clean up everything after itself?
If the application creates data files, where are they stored by default? Does the application remove them at uninstallation? Should it?
Then you may have issues with setup such as what options do in the installer.
That's just a place to start. Its by no means the end to installation testing. Depending upon if you are deploying to Windows, Mac, Linux, Android, iOS, or something else you might have additional informed questions based on how the app works in that environment.