Why does deleting a Mac OS X app leaves its shortcut in the Launchpad? Whenever I delete an app from the Applications folder, its shortcut stays in the Launchpad. In order to delete it, I have to click on it (a question mark appears), and then drag to the trash can. Is it a bug, or does this mean I am doing something wrong?
It may be a bug, but I am thinking it may mean your Spotlight index is corrupt. 

I just tried deleting Evernote from my Applications folder. After authenticating, it moved it to the trash. I then checked launchpad again, and it was no longer there. Then, when I dragged it back out of the trash and placed back into Applications folder. Relaunched launchpad, and it was there again on the last page. As in, worked as expected here. 

Launchpad keeps its own plist of what files there are, etc, and thats why there are some modification tools to allow to you to edit it. But I am assuming they would use spotlight to 'watch' your Applications folder to add new items not through the Mac App Store. I assume Spotlight because its a great tool for the job, installing Lion does a huge spotlight re-index, and they do use spotlight often behind the scenes. 

First, the GUI way I have seen online is to do this (I do the command line way below):


In system's preferences -> spotlight -> Privacy add the drive you want to re-index
Quit System's preferences
Logout of your sessions
Login again :-)
In system's preferences -> spotlight -> Privacy remove the drive you want to re-index
Wait.. a faily long time. You should see mdworker and/or mds running


Personally, I have always done it through the command line. 


Launch ‘Terminal’ (located in /Applications/Utilities/) 
At the command prompt, type this exactly: sudo mdutil -E / 
You will be asked for your password, provide it, as this command requires
administrator privelages to run 
You will receive a confirmation message saying that index will be rebuilt 
Wait until index is finished rebuilding, this can take a while depending on the size of your hard drive, amount of files, etc.


While I can't find any documentation online that 100% confirms that Launchpad uses Spotlight for this, this would be the first place I would look for the problem you are having.