IOS – How to create a desktop icon for downloaded iOS apps (“Find My Friends”)

Back up your iPad to your computer or iCloud, and pull a factory reset on the sucker. I know that some people have been having issues with iOS 5.0.1, and that a complete wipe/reset is necessary to fix some issues. I hope this helps, and good luck!

You don't have to use Launchpad to remove applications. Just deleting the application bundle is still a supported way to remove or uninstall an application. If you also want to remove settings or cache files, delete the directory in ~/Library/Containers/. App Store applications are not allowed to install kernel extensions or preference panes, and any executables for helper processes are inside the application bundle and not in an Application Support directory.

When you remove an application from Launchpad, it is "uninstalled" by using uninstalld from Uninstall.framework, but in practice that only removes some support files (like ~/Library/Containers/*/Data/Library/Caches/) addition to the application bundle. Other support files like preferences files or sometimes even sqlite files for user data are not removed. See this question.