Hi Danny,
Thank you for posting your query in Microsoft Community!
I understand that uninstalled app is still shown in the app store.
Please whether the apps are shown in the All apps window.
I suggest you to follow the steps given below and check if the issue persists.
Method 1: Reset Windows Store cache
a) Press the ‘Windows + R’ key on the keyboard.
b) Type "Wsreset.exe" and press Enter.
Check if the issue persists, if yes, please perform a clean boot.
Method 2: Perform Clean Boot.
To help troubleshoot error messages and other issues, you can start Windows 8 by using a minimal set of drivers and startup programs. This kind of startup is known as a "clean boot." A clean boot helps eliminate software conflicts.
http://support.microsoft.com/kb/929135
Important: Reset the computer to start as usual.
Note: After you have finished troubleshooting, follow these steps to boot to normal startup.
a) Press the ‘Windows + R’ key on the keyboard.
b) In the ‘Run’ windows type ‘MSCONFIG’ and click ‘Ok’.
c) On the ‘General’ tab, click the ‘Normal Startup’ option, and then click
‘OK’.
d) When you are prompted to restart the computer, click ‘Restart’.
Also refer the link given below,
"Why can't I find or install an app from the Windows Store?"
http://windows.microsoft.com/en-US/windows-8/why-find-install-app-windows-store
Hope the information helps! If you need any further assistance, please post. We will be glad to help.
